2012-labman

Brey/Claver ISU Physics-4416/5516 Spring 2012 1

HPHY 4416/5516: Introduction to Nuclear Measurements Richard Brey, Ph.D., C.H.P.

Kevin Claver Our mission is educating students so they can achieve the highest standards of the health physics profession, and solving important problems for the people and industries of Idaho and the Nation through teaching, research, and service. The educational objectives of the ISU Health Physics program are to produce Health Physicists with

1 ) broad, fundamental technical knowledge, 2) written and verbal communication skills 3) professional judgement and capability to think critically 4) practical experience in solving applied health-physics problems 5) the ability to work independently 6) a professional ethic

of magnitude sufficient for them to productively and successfully work in a variety of health physics settings. Description: Lecture/laboratory course emphasizing practical measurement techniques in

nuclear physics. Expectations: The Idaho State University Health Physics Program participates in ABET

Accreditation. This class serves to partially address the following curriculum areas under AProposed Program Criteria@ Section I and Section II, respectively, for Baccalaureate and Masters Level Programs: #(3) radiation detection and measurements with laboratory experience, #(5) principles of radiation safety and health physics. This class will also in part address all 6 of the ISU educational objectives listed above.

Class time: Class 7:00- 9:50 PM, Tuesday - All students must also sign up for a laboratory section

Location: LIBR 16, CHE 208 Text: Required Text for class:

Radiation Detection and Measurement: Glenn Knoll (Latest edition) Suggested texts:

1) Measurement and Detection of Radiation: Nicholas Tsoulfanidis (latest edition) 2) Techniques for Nuclear and Particle Physics Experiments W.R. Leo (latest Edition)

Required: Laboratory Notebook Laboratory handouts

Instructor: Richard R. Brey, Ph.D., C.H.P. Kevin Claver Professor of Physics Physics Instructor PS 123B PS 106B/B108 282-2667 (office) 282-4558 282-4649 (fax) 282-4649 (fax) [email protected] [email protected]

Office Hours: Brey: 10-11, Monday - Thursday Claver: By Appointment


Disabilities: Our program is committed to all students achieving their potential. If you have a disability or think you have a disability (physical, learning disability, hearing, vision, psychiatric) which may need a reasonable accommodation, please contact Disability Services located in the Rendezvous Complex, Room 125, 282-3599 as early as possible.

No materials from this manual can be copied without prior express written permission from the author. Copyright © 2012.


Topical Section 1. Brey Laboratory Radiation Safety and use of the oscilloscope No report 2. Brey NIM equipment and the GM-tube

a) Characteristic curve 3. Brey GM-tube experiments

a) Counting statistics b) Propagation of error c) Environmental samples

i) integral mode ii) differential mode

b) Beam Attenuation Analyses 4. Brey GM-tube experiments

a) Half-life b) Back-scatter c) GM-tube dead time corrections Report 1 all GM

5. Brey Proportional counters a) Determination of operation plateau b) α and β discrimination c) Quantitative analysis of an unknown

6. Brey Proportional Counters

a) Air filter analysis Report 2 all prop. 7. Brey Ionization chamber calibration demonstration

a) Radiation survey b) radiation contamination survey No report

8.Brey Scintillation detectors (Report combined with Lab 9: Scintillation Detectors and MCAs) a) SCA experiments

Midterm will be a laboratory practical - TBA 9. Brey Scintillation detectors

Scintillation Detectors and SCAs) a) MCA

i) energy calibration ii) efficiency calibration

b) GAMMA Spectrum study c) Activation analysis Report 3 all Scint.

10. Brey High Resolution Gamma Spectroscopy a) Energy calibration b) Efficiency calibration Report 4 all High Res.

11. Brey Surface Barrier Detectors a) Alpha spectroscopy b) Energy Straggling Report 5 alpha spec.


12. Brey Liquid scintillation a) Quantitative analyses b) tracer experiment Report 6 all LSC

13. Brey Neutron Detection Techniques Report 7 all neutron 14. Brey Thermoluminescent dosimetry Report 8 TLD 15. Laboratory Final

Class Policy: Grading:

Laboratory Reports 50% Quizzes 10% Laboratory note books 10% Individual Laboratory Practices (Midterm) 10% Final 20% 1) Attendance is mandatory for all laboratory sessions. NO MAKE-UP laboratory sessions are planned. 2) All radiation safety and electrical safety procedures will be followed during laboratory time. 3) Pre-laboratory quizzes will be given randomly. These must be passed or students will not be allowed to participate in laboratory sessions. 4) Laboratory reports must be turned in on time. At the discretion of the laboratory instructors any late reports may be rejected.

A. If late reports are accepted, they will be lowered by one letter grade (essentially 10%) for each week over due. B. No laboratory reports will be accepted after 9:00 AM on the Monday morning beginning finals week. C. The due date of the report is the beginning of your assigned laboratory session - two weeks after the topical section finishes excepted as limited by item AB@ above.

5) A laboratory notebook must be maintained by all students. INCLUDES:

A) Pre-lab write-up B) Experimental set-up C) Experimental Procedure D) ALL data

6) A formal laboratory write-up is required for each lab session as indicated above.

A) A specific format must be followed B) Spelling, grammar, and style will all be assessed.


Laboratory Report Format : Title Page: Include your Name, Partner=s Name, Title(s) of Experiment, Date Due, and Dates Performed. Abstract: This section includes the purpose of the experiment, a short summary of the experimental method, and a brief summary of results. Introduction: This section explains the purpose of the experiment, background and theory. This may briefly describe expected results based upon theory. Explanations of theory and the introduction of equations is appropriate in this section. Methods and Materials: This is the detailed experimental procedure. This gives enough detail to reproduce the results of the experiment. It is appropriate to show schematics, sketches, and flow charts in this section. Too much detail, however, is not appropriate. This section is not a minute-by-minute log of the events that have occurred during your experiment. Such details should be found in your log book. It is appropriate to describe formal hypothesis tests (if any) that will be addressed by this experiment. These are the a priori hypothesis that you are testing with your experiment. You should formally list the hypothesis, the alternative hypothesis, the statistical decision rule and the criteria for rejection of hypothesis. Results and Discussion: This is where results and explanations of the results are reported. Critical elements to address are data uncertainty and data completeness. A discussion of the measures of uncertainty are appropriate in this section. Show methods for the propagation of error in appendices. Tables of data should be provided in a publishable format and should include data uncertainty. Plots of data must show error bars. Any trend lines or fitted curves should be described mathematically, along with statistical descriptors of the quality of the fit of data. If poor quality data are obtained, their explanation should be based upon plausible physical phenomena. The split source method of dead time determination, for example, may fail due to low activity of sources. On the other hand, we are not interested in blunders. Instead, they are to be corrected during the experiment. Problems with the reproducibility of experimental geometry, for example, are issues of poor technique and should be resolved during the experiment. Results of hypothesis tests, when appropriate, should also be reported here. Conclusions: This is a very brief section (1 or 2 paragraphs) that address the primary Afacts@ you can Aprove@ based upon your data, further work or refinements that could improve your measurement, questions that arise because of your data, and brief answers to any questions that are at the end of your lab handout.

Important Reporting Items:

1) Reports must be typed or word-processed. Use complete sentences, appropriate grammar, and write in the third person past tense. If you use a reference source, please


provide this reference in a list of references at the end of the report.

2) Use the format of either AHealth Physics@, ANuclear Instruments and Methods in Physics Research@ or Physical Review C: Nuclear Physics@ for your reports. All three of these journals are in the physics office (ask Sandra or Ellen) and all three describe the proper format at the back of the journal.

3) General style issues: Avoid starting sentences with prepositions. Avoid pronouns because pronouns frequently lead to loss of clarity. Don=t end sentences with pronouns. Be careful with the number of significant figures.

4) A good source on scientific writing and presentations is AScientific Papers and Presentations@, by Martha Davis, Academic Press, San Diego, CA 1997. ISBN 0-12-206370-8 (Ellen Nelson has several of these in her office that may be loaned to students for short periods of time)


Laboratory reports will be graded using the following grade work sheet: Name Mr. X Partner Ms. Y Lab Experiment Name

(10 pts possible) (10 pts possible) (10 pts possible) (10 pts possible) 5 points SUB Total Concise Grammar and Spelling Organization and Structure Technical Present

Title Page x x x x 5 5 Abstract x 0 Introduction x 0 Methods and Materials x 0 Results and Discussion x 0 Conclusions x 0

Maximum Possible 205 Grand Total = 5

Grade

=

2.4


Use of the Oscilloscope OBJECTIVES: The objective of this laboratory exercise is to become familiar with the operation and use of the oscilloscope.

INTRODUCTION:

An oscilloscope is a device which measures voltage as a function of time. The major components of an oscilloscope include a cathode ray tube (for visual observation of signal), sweep generator, two amplifiers, and various power supplies.

Components of oscilloscope:

Figure 1.

The most obvious component of the oscilloscope is the cathode ray tube

(CRT). The figure 1 is a schematic of a CRT. The cathode is heated which liberates electrons from the surface of the cathode. The accelerating anode is used to provide a high potential difference with respect to the cathode. The electric field resulting from this potential causes electrons given off by the cathode to accelerate towards the anode. The accelerating anode has a hole in it which allows the electrons to travel through with constant velocity. These electrons eventually strike the fluorescent screen which creates a bright spot on the display.

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The focusing anode is used to shape the electric field pattern between the cathode and accelerating anode. This is done by varying the potential of the focusing anode with respect to the accelerating anode. This focuses the stream of electrons into a "tight beam".

The control grid is a metal screen which has a potential difference relative to the cathode that can be varied to control the number of electrons reaching the anode. This in turn controls the brightness of the display on the screen.

To steer the electron beam, two sets of deflection plates are used to direct the beam toward a location on the fluorescent screen. The horizontal deflection plates control vertical deflection of the beam. The deflection experienced by the beam is directly proportional to the potential difference between the plates. A voltage signal fed into the oscilloscope passes through an amplification circuit which is applied to the deflection plates. The amplifier setting determines the vertical deflection which is directly proportional to the signal. The amplifier for the horizontal deflection plates is controlled by the knob marked VOLTS/DIV on the front of the oscilloscope.

The vertical deflection plates control horizontal deflection of the beam. The potential difference between the vertical deflection plates is controlled by a sweep generator. The sweep generator varies the voltage to vertical deflection plates in such a manner that the electron beam "sweeps" from left to right across the display. This "sweep" cycle repeats itself continuously during oscilloscope operation. The knob marked SEC/DIV on the front of the oscilloscope controls the rate at which the electron beam "sweeps" across the display screen. This "sweep" of the electron beam is referred to as the trace.

Controls

The vertical controls on the oscilloscope control the vertical position of the trace as well as the voltage required to move the trace vertically. The input signal may either be positive or negative with respect to the baseline position. Oscilloscopes often have provisions for two input signals to be observed simultaneously. Each input has its own set of controls for position and amplification.


The horizontal controls consist of a position control and a gain control which is often calibrated in centimeters per unit of time. The position control moves the start of the trace or signal to any position on the display screen. The gain control permits one to vary the time/distance of the horizontal axis from periods as long as seconds to fractions of seconds.

The trigger controls are used to start the trace at the beginning of the electronic signal. The input to the trigger circuit can be from the internal (vertical) input, the 60 cycle line voltage (trace starts every 16.7 milliseconds), or an independent external signal. If the trigger circuit is set to trigger on the internal mode, the trigger waits until a signal appears on the input to the vertical amplifier. When the vertical signal has reached a certain voltage level, determined by the trigger level, the trigger starts the horizontal time sweep and starts to display a signal on the display screen. The trigger system can be activated by a positive or negative signal. In such cases, the system must be told which type of signal to expect. The automatic triggering mode will trigger on any small voltage rise on the input to the vertical amplifier. This mode often triggers on electronic noise and produces trigger signals which may not be of interest to the experimenter. Signals

Certain features of electronic signals are always of interest (e.g. rise time, decay time, pulse width, pulse amplitude, if signal is repeatable, frequency, or time between pulses). Rise time (tr) is the time interval between 10 and 90 percent of full amplitude. Decay time (td) is the time interval for the pulse to drop from 90 to 10 percent of the absolute amplitude. It is not uncommon for electronic signals to have different rise times and decay times. The width of the pulse can be taken either as a time interval between the 10 percent level of the rise time and 10 percent level of the decay time, or it can be taken as the width of the pulse at one half of the maximum height. Whichever width is used for the pulse, the definition that is being used should be noted.

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Figure 2. A sketch of the shape of the pulse will provide a great deal of information along with the rise time, decay time, and pulse amplitude. Therefore, it should become a habit to always sketch the shape of the pulse and mark the various parameters of interest on the pulse. Refer to figure 2.

PROCEDURE: 1) Sketch the front of the oscilloscope in your laboratory notebook. Note the locations of controls used and identify the type of oscilloscope used. Connect function generator output to the oscilloscope Y input. Be careful to use the proper connecting wire and do not force connections. Set the triggering for the oscilloscope for a line source in normal mode. Set amplification setting for horizontal deflection plates (VOLTS/DIV) at 0.5 for the x1 probe. 2) Set the function generator to the following parameters. Set the frequency to 1000 Hz (x1K), continuous trigger mode, wave form needs to be a sinusoidal, set sweep time to 1 s, and the amplitude to 1 Vpp. 3) Determine the SEC/DIV setting where only one complete wave (cycle) fits on the oscilloscope display (sketch the display). What is the period for this wave? 4) According to your sketch of the wave, how many divisions does the amplitude exhibit? Does this correspond to the amplitude of the output wave form produced by the function generator? Explain. 5) Change the amplitude of the output wave form produced by the function generator to 3. Sketch the display. What is the period for this wave? 6) According to your sketch of the wave, how many divisions does the amplitude exhibit? Does this correspond to the amplitude of the output wave form produced by the function generator? Explain.


7) Change the amplitude of the output wave to 10 Vpp on the function generator. Adjust the VOLTS/DIV knob until the full wave just fits on the oscilloscope display. Record corresponding multiplier from the VOLTS/DIV knob. Sketch the displayed wave. Using your sketch (or oscilloscope display), determine the number of divisions corresponding to the magnitude (corresponding to the nearest tenth of a division) of the wave's amplitude. Multiply the amplitude by the multiplier on the VOLTS/DIV knob. Record the value. 8) Repeat step 1-7 using function generator output frequencies of 10K, 100K, and 1M cycles per second and the 15 MHz oscilloscope. 9) Repeat step 1-8 using an oscilloscope different from the one used in the first step.

10) Change the wave form produced by the function generator to the square wave function. Set the frequency to x1K and the amplitude to 1. Set the trace to 2 ms/div and the vertical deflection amplifier to 0.5 volts/div. Sketch the shape of the wave on the oscilloscope display.


NIM equipment and the GM-tube OBJECTIVES

1) The student will understand the benefits of equipment based on the NIM standard, and basic NIM features. 2) The student will be able to describe common modules and their purpose. 3) The student will be able to identify all gas detector regions of operation. 4) The student will understand and be able to calculate the value of resolving time for a gas detector. 5) The student will understand concepts of resolving time, recovery time, and decay time. 6) The student will know how to develop a characteristic curve for a GM detector and determine the proper operating voltage for this type of detector.

INTRODUCTION I) The NIM and CAMAC instrumentations standards The two most common instrumentation standards in use today within the nuclear industry are the NIM standard and the CAMAC standard. The acronym NIM stands for Nuclear Instrumentation Module and the acronym CAMAC for Computer Automated Measurement and Control. NIM equipment seems to be the most common of the two around radioanalyses laboratories. During this semester we will exclusively consider the NIM standard. There are several advantages associated with the NIM standardized system of instrumentation. The NIM instrumentation system has the following attributes:

1) All NIM equipment is manufactured using standardized dimensions. The standard width is 1.35 inches (34.4 mm) and all NIM modules have a width which is equal to or multiples of this standard module size. There are two possible heights of modules according to the NIM standard. The most popular module height is 8 and 3/4 inches (222 mm), modules with a height of 5 and 1/4 inch (133 mm) are also available. These modules are constructed such that they all may fit into a housing called a bin (a NIM bin) or crate. All modules and bins which meet the NIM standard are mechanically interchangeable.

These modules additionally share a standard system of coaxial cable connectors. It is convention, according to Knoll (1989), to refer to connectors as either plugs or jacks corresponding to male and female types, respectively. SHV connectors are the most commonly used for high voltage jacks but also one frequently finds MHV connectors used as high voltage jacks. BNC connectors are most often used for


signal jacks. Either panel jacks, which are screw mounted via and attached flange, or bulkhead jacks, which are tightened in a panel cut out using a nut and lock washer, are mounted on the NIM modules. The coaxial cables which connect modules typically have plugs at both ends.

These features allow rapid replacement of compartmentalized individual components which happen to fail. They enhance the availability of equipment. They decrease equipment down time in most cases. These features also hasten trouble shooting efforts.

2) Generally, only the bin is connected to laboratory ac power and it provides all the necessary dc voltage required by the modules used. The primary dc supply voltages provided by most bins are """" 24 volts and """" 12 volts. Sometimes bins may also be wired to provide """" 6 volts but this in not a NIM requirement. As a general rule the bin acts as the power supply for most NIM modules.

One exception to this generalization is that of high voltage power supplies. Occasionally, one encounters high voltage power supplies which have their own power cord. They require an independent source of power not supplied by the NIM bin. There are two types of such high voltage power supplies. One type is completely independent of the bin. This is generally wide enough to be mounted in a 19-inch relay rack or cabinet. These usually are between 3 and 6 inches tall. The second type has the normal NIM module dimensions and fits into a standard NIM bin.

3) Nim standards specify the polarity and magnitude of both logic and linear pulses. This allows one to develop expectations for the types of pulses which must properly be fed into the modules and which should properly be produced. This feature simplifies trouble shooting efforts.

Disadvantages of the NIM system include an inability to handle large volumes of digital data and in cases of simple modules a tendency for excessive module size requirements.

Common NIM components

A) Preamplifiers Radiation detectors usually produce current pulses. These are typically quite small often in the millivolt or even microvolt range. The first steps in signal processing must therefore be to both convert the current pulse into a voltage pulse and increase the magnitude of the signal so that it is not lost in


transmission.

These goals are accomplished with a preamplifier. The preamplifier output is designed to be used by NIM instruments. The preamplifier should be placed as close as feasible to the detector thereby using the shortest possible signal capable. This decreases capacitive loading and helps to enhance the signal to noise ratio. The preamplifier "conventionally" provides no pulse shaping but it does function to terminate the detector capacitance quickly. This also enhances the signal to noise ratio. The preamplifier presents a high impedance to the detector but a low impedance tail pulse output. Hence, it provides impedance matching. The rise time of the preamplifiers output pulse is kept as short as possible, nearly equivalent to the charge collection time in the detector itself while its decay time is long usually on the order of 50 or 100µs. A long decay time ensures full collection of the charge from a wide variety of detectors prior to excessive pulse decay.

A preamplifier is not necessary in all detector systems. A GM counting system for instance has a large enough output pulse from the detector to make a preamp unnecessary. However, prior to placing the output of a GM tube directly into either an amplifier, an SCA, or a scaler it is first necessary to decouple the signal from the high voltage which maintains the high potential between the tube's anode and cathode. This is usually achieved using a simple RC circuit. The black boxes which the GM tube bases are plugged into in our laboratory serve this purpose. Sometimes scintillation crystals operated with higher gain photomultiplier-tubes may be operated without preamplifiers particular if they are to be used for simple photon counting applications. When a preamplifier is used in a system, often the detector signal is so small that there is no way that its shape can be checked with an oscilloscope, only the output of the preamplifier can be monitored.

B) Amplifiers

The next component in a signal train is an amplifier. This may or may not amplify the signal depending on the size of the detector output pulse for the same reasons discussed above. If the amplifier must amplify the signal it is capable of doing so by factors of 1000 or more. In either case the amplifier will shape the pulse and provide noise filtering for the system.

The amplifiers for processing signals in nuclear detector systems are referred


to as linear amplifiers because their output is proportional to their input. These require either a positive or negative input signal with a fast rise time usually less than one microsecond and a long decay time greater than thirty microseconds. The output pulse of these types of amplifiers, in these applications, has a Gaussian shape.

Most amplifiers are capable of producing either a unipolar or bipolar output pulse. Some amplifiers are capable of producing both types of pulses simultaneously out of two different output jacks. Others with only one output jack use a switch which allows one to select the output pulse of choice.

A unipolar Gaussian shaped pulse is a positive, approximately symmetrically shaped pulse, with rise and decay times varying from one to six microseconds depending on the time constant used in the amplifier and to some extent on the rise time of the input pulse. The bipolar pulse will have a positive lobe followed by a negative lobe. The width of the positive portion of the bipolar pulse will be about one half of the width of the unipolar pulse. The area of the positive and negative portions of the bipolar pulses are equal.

The amplitude of the output pulses vary from 0 to 10 volts. If the wrong polarity input pulse is used, the polarity of the output pulse will be reversed. Most of the signal processing equipment used in line after the amplifier expects a positive pulse.

C) Signal Channel Analyzers

Signals from nuclear detectors carry information. This information may be about the time at which an event occurred, the amount of energy deposited in the detector, or simply that an event did indeed occur. When considering the amount of energy deposited within a detector the information of most importance is the size or amplitude of the signal. This information can be evaluated with a single channel analyzer.

Commonly, single channel analyzers (SCA) may operated in one or two completely different types of modes. These are the "integral" modes and the "differential" modes. Occasionally, one may observe SCAs' which operate in a third mode referred to as a "normal" mode.


The integral mode is the simplest mode of operation of a single channel analyzer. An integral discriminator is simply a trigger circuit that will send out a uniform logic (or square wave) pulse between 2 and 10 volts whenever an input pulse exceeds the preset baseline discrimination level. The same output pulse occurs no matter how much the input pulse exceeds the preset base line; that is, if the input exceeds the base line by 0.01 volts or 5 volts, the output pulse will be the same.

The differential discriminator mode sets a window, with a lower level discriminator or base line and an upper level discriminator. This is sometimes referred to as the "window" mode. Because the difference between the upper and lower levels is called the window. A standard output logic pulse between about 2 and 10 volts is generated only if the input pulse exceeds the lower level or base line discriminator, and does not exceed the upper level discriminator. Although, the level of the two discriminators can usually be adjusted independently, most differential discriminators have provisions for setting the upper level discriminator a fixed voltage above the baseline and to keep this difference constant as the base line voltage is changed. The upper level window is said to ride on the baseline discriminator. This greatly simplifies the use of the single channel analyzer as will be shown in later experiments.

The "normal" mode which is sometimes included on certain SCAs' is similar to the differential mode in that they both establish a window which discriminates against pulses which are too small or too large. The difference in this situation is that the two discriminators are completely independent of one another.

The output pulse of a SCA is always a logic or square wave pulse between about 2 and 10 volts. The amplitude depends on the instrument. This output is the same size regardless of the input pulse size.

D) Timers and scalers.

Timers and scalers typically form the end of the pulse train and convert the signal to some sort of useful information. These are not the only possible uses of the signal. Timers and scalers may be independent NIM modules or integral components of one module.

The scaler counts the number of pulses or signals produced in the system. Scalers are simply very fast counters. Scalers often have discriminators which allow one to exclude small noise pulses from being counted. The scaler


may be "turned on" or "off" either manually or auto matically. Manual control is often performed by a simple button or switch on the front panel. Automatic control is usually accomplished by means of an external logic single fed into the scaler via a "gate" jack which may be located on the front or back panel.

The external logic single is typically produced as an output pulse from the timer. The timer is just a high precision stop watch. An increment of time is selected the timer is engaged and it produces a logic pulse until the selected time has elapsed. There are many different types of timers available for use. The student is encouraged to study the panel indications of each timer used and then briefly experiment with the particular systems operation. Timer operation is often intuitively obvious.

During this semester undoubtedly many other types of NIM equipment will be used. The components described above however form a central core of items which will be used over and over again.

II) General operation of gas filled detectors and the GM tube A) Gas filled detectors Generally, radiation detection instruments do not detect radiation directly. What these instruments detect is the interaction of radiation with the material in the detector. This material is commonly, but not exclusively, gas. Most gas filled detectors consist of three parts: a detector, some sort of amplification system, and a measuring device. The output of the detector is manipulated; often the output pulse is shaped and amplified, and then converted to a useful measurement observed via the measuring device. The operation of a gas filled detector depends on radiation ionizing the gas molecules within the detector chamber producing ion pairs. The detector chamber consists of a positive anode, often a thin wire running through its center, and a cathode, typically the outside wall of the chamber. The anode and cathode are electrically insulated from one another. During operation, the anode is maintained at a high positive potential commonly hundreds or thousands of volts. The cathode is normally maintained at a negative potential. As a consequence, an electrical field is experienced by charged particles existing within the detector's chamber.


Ion pairs, usually an ionized electron and the positively charged remainder of the ionized molecule, which are generated within the chamber by ionizing radiation, begin to migrate toward the electrodes as soon as they are produced. Electrons migrate toward the anode, the positive ions migrate toward the cathode. The rate of this migration depends on the strength of the electric field. If a low potential is maintained between the anode and cathode and as a consequence a weak electric field is experienced by the ions, they will move very slowly toward the electrodes. Those ions which move very slowly may sometimes recombine prior to reaching the electrodes. When stronger electric fields exist all of the ions generated reach the electrodes. Even stronger fields may move the ions toward the electrodes so rapidly that the ions themselves obtain sufficient energy to cause both excitation and the ionization of molecules they meet on the way. The ion pairs generated in this way migrate to the electrodes. The excited molecules general de-excite with the emission of a light or UV photon within a nanosecond or so. This photon has the potential for liberating a new electron (under the strong electrical field condition in question) which along with its positive counter part migrates to the electrodes. This process contributes to a chain reaction process which will be described during a later discussion of quench gases. The relationship between the applied voltage, i.e. the potential difference between the anode and cathode, and the number of ions collected is well known. Different ranges of potential have been categorized into regions corresponding to the collection of ions at the electrodes. The number of ions collected at the electrodes influences the size of the pulse produced as a consequence of a particular interaction of radiation within the detector chamber. The six-region curve categorizes the relationship between applied voltage and the way ions can be expected to be collected at the electrodes. The six regions are as follows:

1) Recombination region - this applies to very low voltage; as voltage increases, the size of the pulse generated because of an incident radiation's collision increases. However, the number of ions collected is less than the number produced. This region is not useful for detector systems.

2) Ionization chamber region - pulse size does not change as the voltage increases. This portion of the curve is essentially flat. The number of ions collected does not appreciably change over a broad range of applied voltage. Essentially every ion created is collected. The voltage is high enough so that there is no recombination but the voltage is not high enough to impart to migrating ions enough energy to cause further ionization.

3) Proportional region - Pulse size increases proportionally for a given type of


radiation as voltage increases. The number of ion pairs collected is greater than the number created. Some gas amplification, the creation of new ion pairs by the migrating ions on there way to the electrodes, occurs. The gas amplification factor reflects the multiplication of the number of ions collected versus created. For instance, if 5 ions pairs were originally created and the gas amplification factor were 10 than it would be expected that 50 ion pairs would be collected. Operation in the gas amplification region is possible because the gas amplification factor at a specific voltage in the proportional region is the same for any type of radiation or energy of that radiation. This changes for different types of radiation but is consistent within specific radiation types. As long the voltage remains constant the number of ion pairs collected is proportional to the number of ion pairs originally produced.

4) Limited proportional region - Pulse size increases as voltage increases but in a non-linear way. Gas amplification occurs but this changes so rapidly with change in voltage that the region is not useful.

5) Geiger-Muller region - pulse size increases slightly as voltage increases but so slowly as to be unnoticeable over relatively large changes in applied potential. This is because the potential is so high that every event occurring within the detector region leads to the generation of many ion pairs, each ion pair producing more ion pairs as it migrates toward the electrodes. This effect is referred to as an Townsend avalanche. It is the result of the high voltage potential between the electrodes.

When ionization occurs, the negatively charged ions (free electrons), which are much smaller than the positively charged ions, move quickly to the positive electrode. The positively charged ions, which are larger, move much more slowly. In fact, they tend to form a cloud of ions that moves gradually to the negative chamber wall.

The cloud of positively charged ions effectively forms a second "positive electrodes," which actually divides the large voltage potential into two smaller voltage potentials - one between the highly positive central electrode and the positively charged cloud and another between the positively charged cloud and the negatively charged walls. Since these two smaller voltage differentials take the place of the one large voltage differential, two small sub-detectors are, in effect, produced. The voltage potential in either of these sub-detectors is well below the applied voltage of the Geiger-Muller region, so the avalanche stops.

When an avalanche occurs, it is so great that the pulse size does not depend on the number of ion pairs produced by the radiation entering the detector. The pulse size is the same, no matter what type of energy of radiation caused the ionization. Therefore, in the Geiger-Muller region, it is possible to tell that radiation is present,


but, just from the pulse size it is not possible to determine the type of radiation. The GM-tube is considered to be a highly sensitive instrument for the detection of radiation.

B) The GM detector: resolving time and dead time

When radiation interacts with the gas in a detector chamber operated in the GM region it creates ion pairs which rush with high velocity to the respective electrodes. This migration is so fast that they cause further gas molecules to ionize which in turn rush toward the electrodes causing even more molecules to ionize. This Townsend avalanche, sometimes referred to as a Geiger discharge, leads to a momentary collapse of the electrical field induced between the anode and cathode. It also produces a pulse of some maximum size. If a second particle were to enter the detector during the avalanche period, it may or may not produce a pulse. If it does produce a pulse, it may or may not be large enough to be detected. A specific fraction of time is required before the effects of the avalanche of secondary ions had been cleared out sufficiently for a new pulse to be formed which has a great enough magnitude to be detected. The time following an initial pulse during which a second event can not produce a new pulse regardless of its size is called the dead time. Typically for a GM tube this time is between 50 and 100 µseconds. After the original pulse dies out, another full-size pulse can eventually be produced.

The time required for a GM counting system to return to the initial condition - or close enough to it that a second pulse can be created which has sufficient magnitude to be detected - is called the resolving time. The recovery time is the time interval required for the tube to return to its original state and become capable of producing a second pulse of full amplitude. The resolving time also includes the time it takes the electronic counting system to recovery from the process of recording an event. Normally the electronics operate so quickly compared to the tube operation that their contribution to resolving time is insignificant. The terms resolving time and dead time are considered by many to be interchangeable. Although this is true in practice, it should be well known by the student that they have two different meanings.

When considering dead time in more detail, many authors categorize dead time into two different types. These two fundamental cases are: extendable and non-extendable. Alternately, these are referred to as paralyzable and non-paralyzable dead times. The circumstance of paralyzable or extendable dead time occurs when the arrival of a second interaction event during the dead time period of the first pulse extends the initial dead time period, adding its own contribution starting from the instant of its arrival. This produces a prolonged period in which no pulses are created and on events are recorded. The element is thus paralyzed.


This was a particularly dangerous problem with old GM survey instruments which would effectively become saturated in high radiation fields and electronically respond as if no radiation were present. Newer survey instruments have special circuits to avoid this circumstance. GM detectors experience an extendable type of dead time. The non-extendable case of dead time corresponds to detector types which become insensitive during pulse processing. This period is their dead time. They ignore any events occurring during this time span. The arrival of a second pulse in this period simply goes unnoticed. After the dead time period, the detector instantly becomes active again. We will discuss instruments with this capability later in the course.

Once it is established which type of dead time is being experienced and dead time is actually measured it is possible to correct for dead time losses.

Correction for dead time losses is done in the following way.

Let: n = true interaction rate m = recorded count rate τ = system dead time

For a non-paralyzable detector the true count rate "n" is given by the expression:

n = m/(1-nτ)

For a paralyzable detector the true count rate is given by the expression:

n = m/(exp-nτ)

however, because of the "n" which appears in the exponential term this expression becomes cumbersome and is usually solved by iteration. It can be proven that these two expressions have the same limit in the situation of small dead time loss so a simplification of this last expression is the approximation:

n .... m/(1-mτ)

which only applies to short dead time situations.

There are two methods to determine the dead time of a system. We will investigate those methods during this laboratory session. The first is a direct measurement of the width of the GM-tube pulse using an oscilloscope. The second is referred to as the split source method.


In the split source method one has a special source of radiation which is usually in the form of a disk. This disk splits in two halves across the diameter of the disk. First both half of the source are counted this gives a value for the variable n12. One of the halves is removed without disturbing the other. The remaining source is counted, this gives the value of the variable n1. The first source removed is replaced and the other source is removed. The other source is counted to give the value of the variable n2. Ideally, when ever one of the source halves is removed it should be replaced by an equivalent geometry blank. Finally both sources are removed and both blank pieces are counted. to give the value of the variable b. All source combinations and the background are counted for the same length of time. This method works because the counting losses are non-linear, the observed rate due to the combined sources will be less than the sum of the rates due to the two sources counted individually. The dead time can be calculated from this discrepancy as follows:

τ = [(n1/T)+(n2/T)-(n12/T)-(b/T)]/ [2(n 1/T)(n2/T)]

where T is the time of the count (technically referred to as the real time).

The Geiger Counting Plateau

The Geiger counter usually functions as a simple counter so its application requires that an operating condition be established such that essentially each pulse which is generated in the detector volume is counted. This is accomplished by establishing over which ranges of voltage the GM plateau for a particular GM tube exists. This plateau is observed in the general six region curve within the GM-region.

The plateau curve is established by counting a source for a known increment of time and recording the result. The voltage is increased slightly, by 50 volts or so, and the source is again counted for the same length of time. This process is repeated several times. Each time a data point is obtained it is plotted on a curve of count rate on the Y-axis versus high voltage on the X-axis.

At low voltages typically few or no pulses are recorded. The voltage is eventually increased until around 600 to 1000 volts (a detector depend value) to a point were counts start to accumulate. As the voltage is incremented up the count rate increases rapidly for a few increments. Then it reaches a point where it no longer changes. It reaches a plateau. The point where it no longer increases is called a knee. The level point is called a plateau. At further increments of voltage the count rate increases wildly. This is a point of continuous discharge. Do not operate a GM-tube in the continuous discharge region as it will damage the detector.

PROCEDURE:


1) Defining the GM-tube Plateau.

a) Set up the GM-tube and counting equipment as per in class instructions. Be sure to draw this set up, record instrument serial numbers, and describe all lab data in your laboratory note book.

b) With the radiation source provided near the detector, on the specified counting shelf, and the high voltage at 100 volts record the number of counts observed during a 1-minute count time. Record this data point and voltage on a table in your lab note book. Plot this data point on a graph drawn in your note book.

c) Increment the voltage by 50 volts and repeat part (1 b) until counts first climb and then plateau and finally reach the continuous discharge region. The continuous discharge region is typically quite obvious but if not consider yourself there when you exceed an increase above 40% of the average plateau count.

d) Consider the range of voltages spanned by the plateau. The curve's knee is the beginning of this range, the start of the continuous discharge region is the end of this range. The desired operating voltage is about 1/3 the way along this range. Record this operating voltage and set the high voltage at this value.

e) Explain why this plateau exists.

2) Dead time determination

a) Using an oscilloscope obtain a trace of the detector output pulse. Record all information about this trace including all oscilloscope settings. Draw this trace in your note book.

i) What is the width of the output pulse. This width is a good approximation of the tube dead time.

b) Obtain a split source. Make all the recommended counts using the split source and calculate the dead time using the split source method. Which of these two methods do you think is better and why?

Items to contemplate

1) If I performed a 5 minute count of a source on the equipment used during this lab and observed 1,555,792 counts, what would the true count rate actually be?


2) How do the values for these two methods of determining dead time compare.


Accuracy, Precision, and Error Measures of Central Tendency and Statistical Distributions Nuclear Counting and Error Propagation of Error OBJECTIVES

1) Students will develop an understanding of descriptive statistics and hypothesis testing with respect to radioactive decay and radioactivity.

INTRODUCTION When we speak of error we are referring to the difference between the true value of a physical attribute and the value of our measurement of that attribute. We can never really know the "true" value of such a physical attribute. We can estimate a best value for the magnitude of the item in question and we can measure the variability associated with our measurements. In science when we express the measure of a physical attribute we should properly also provide some measure of the variability associated with the measurement. When we provide a measure of variability along with the best estimate we are implicitly describing how "good" of a measurement was made. The variability we measure is the error of the measurement. Every measurement made contains an element of error. Consider a hypothetical experiment in which a group of 20 people are each asked to independently measure the mass of a particular set of three samples using a laboratory balance. We will presume that this particular group of people has had no previous experience with the balance, nor with standard laboratory practices. Some of these people, lets call them group "1" will be very methodical. Some people, lets call them group "2", will make the measurement correctly, for the most part, but perhaps perform the measurements in a consistently sloppy fashion. A few of the people, who will be called group "3", will probably use the balance incorrectly. The set of 20 data points obtained from this experiment could very well exhibit three different types of error. The first type of error is referred to as random error. This type of error is likely to be associated with data from the individuals in group "1". Random errors are the unpredictable and unknown/unmonitored variations during the measurement. Sources of random error include unpredictable fluctuations in electrical power, equipment vibrations, changes in temperature, and interpretation of measured output. For example, was the measurement 8.6675 or 8.6674 grams? Statistical methods may be used to describe random errors. Random errors are inevitable. They can be reduced, but never eliminated completely. The second type of error is referred to as systematic error. This type of error is likely to be associated with the data from individuals in group "2". For example, these people might hypothetically not have cleaned the balance's pan. Particles of a foreign material would have been weighed along with the samples in this situation. Although the values


obtained correctly reflected what was weighed, they were systematically incorrect because they included the weight of the foreign object as well as that of the samples. If the source of systematic error is discovered, the faulty data may often be corrected. The systematic error mentioned in this paragraph may be corrected by finding the mass of the foreign material consistently left in the balance's pan and subtracting it from the data recorded initially. The third type of error falls into the category of unforgivable blunders. These include mistakes of reading instruments incorrectly or using instruments incorrectly, number recording mistakes such as digit transpositions, and arithmetic mistakes. Strictly speaking, these are not true errors. Blunders can be eliminated by working carefully. This type of 'error' is likely to be associated with the data from the individuals in group "3". Hugh D. Young in his book Statistical Treatment of Experimental Data (McGraw-Hill Book Company, Inc. New York, 1962 - page 3) points out that: "The terms accuracy and precision are often used to distinguish between systematic and random errors. If a measurement has small systematic error, we say that it has high accuracy; if small random errors, we say it has high precision". Consider three marksman; Jim, Mark, and Rich. Jim shoots his rifle at the target. The first shot is 15 cm above the bull's eye. His second shot is 17 cm below the bull's eye. His third shot hits the bull's eye. His last shot is 14 cm to the left of the bull's eye. Jim's shots may be considered accurate but not very precise. They demonstrate a high degree of random variation or in other words a high degree of random error. He may have little of almost no systematic error in his technique. Mark shoots four bullets. They all hit the target within a 1-cm circle 30 cm to the left of the bull's eye. Mark may be said to shoot with great precision but poor accuracy. His technique has low random error but obvious systematic error. Rich shoots four bullets. All four hit the target within a 1-cm circle at the center of the bull's eye. We may say that Rich shoots with high precision and high accuracy. His technique demonstrates both low systematic and random error. Descriptive Statistical and Statistical Distributions It was expressed that one could provide a best estimate for the "true" value of the magnitude of a physical parameter. Sometimes this is referred to as the value of the central tendency of the measurement. There are three common parameters which are used to express this concept of central tendency; the mean, median, and mode. When the value of a measurement is reported, it is reported along with an estimate of its error. Ideally this error should mainly reflect random error. This is because systematic errors should be eliminated. One may reduce the magnitude of random error but it can not be eliminated. Descriptive statistics are used to characterize the variability of an error measurement. The variability or error about the measure of central tendency may follow several different distribution functions representing different kinds of randomness. These distributions have slightly different properties.


The mean or arithmetic average is perhaps the most common parameter used in expressing

the central tendency of a measurement. The mean is expressed as: The mode is the most probable value of a parent population. It occurs the most frequently. It is the value most likely to be observed. The median of a finite parent population is defined as that value for which half the observations will be less, and half the observations will be more. The probability is 50% that any observation will be larger or smaller than the median. There are several standard models which describe the variability expected under different situations of random sampling. The three models most commonly used during laboratory data analyses are the binomial, the Poisson, and the Gaussian distributions. Each model describes a particular physical process. All three of these models are related when considering their physical limits. There are specific functions known as probability density functions which apply to each model. These functions are mathematical descriptions of the distribution of random events associated with each model. Consider a series of random events. There is likely to be an underlying physical process governing the occurrence of these events. Each of the three common statistical models describe a particular underlying physical process. Therefore, it is likely that one of the probability density functions associated with these models may be able to describe the frequency of outcomes associated with a series of random trials of one of these processes. We will not consider the details of the probability density functions. But it is important for the student to understand that the frequency distribution of most physical processes are well defined. One can take advantage of this description, the probability density function, to determine the probability of a particular outcome. The student is encouraged to review Chapter 3 of the required text for this course: Radiation Detection and Measurement by Glen F. Knoll for further description of basic physical processes. Other good references include Hugh D. Young's book mentioned previously, or the book by Philip R. Bevington: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, Inc. 1992. The basic properties of the binomial, Gaussian, and Poisson distributions are important to know in order to understand their general application. During this laboratory session the properties of most importance include an expression for the mean and variance of each population. The following table gives the appropriate expression for the mean and variance for each of the distributions under consideration.

x =

n

ji=1

xi

n


Table One Distribution Expression for Mean Expression for variance Binomial np np(1-p) Poisson pn pn Gaussian Σ(xi)/n Σ(xi-x)/(n-1) Here xi represents a sample's outcome from a set of n experimental trials. The variable p represents the probability of a particular type of outcome. We should notice that the mean for the binomial and Poisson distribution are identical. If we were to consider a processes where the probability of an individual outcome is very small than in this limit the binomial distribution would have the same variance as the Poisson distribution. This is particularly true if the mean value of the distribution is large (typically greater than 20). An example of this is the case of radioactive decay. If we consider a series of time increments, we can say that the probability of a particular decay occurring in any particular time increment is very small, and that the probability in any particular increment is the same as in any other increment. In the case of rolling either a one or a six when rolling a die (the singular for dice) we have a similar situation, but the probability for a particular event is quite high, 1 in 6 in fact. So we have similar situations, the process of rolling a die is described better using binomial statistics. Radioactive decay is normally better described using Poisson statistics. All of these distributions may be referred to as normalized distributions because the sum of all the probable outcomes for all events is equal to 1.0. This tells us that the event will eventually occur. It is equivalent to saying that the probability of death is 1.0 - or everyone who is born will die. Obviously the time dependent frequency of these occurrences is not known. Everyone will eventually die but we don't know exactly when a particular individual in the population will expire. A partic ular radioactive atom will decay, but the probability that it will decay within a particular time increment is small. Rolling a one or a six will eventually occur, but rolling a one should occur with a probability equal to 1/6 which is equal to the probability of rolling a six. The probability of rolling either one is 1/3.


Another interesting aspect to the Poisson distribution is the relationship between the mean and the variance. As seen in the table given above, the mean is equal to the variance. The variance is a measure of the width of the distribution. Another measure of the width of a population is the standard deviation. The standard deviation by definition is equal to the square root of the variance. We know that 68% of all events in any distribution will fall within a range of one standard deviation of the mean of that distribution. Further, a little over 95% of the events will fall within two standard deviations of the mean, and more than 98% of the events will fall within three standard deviations of the mean. Since, in the Poisson distribution the variance is equal to the mean, then the standard deviation must be equal to the square root of the mean. If a radioactive sample is counted for an increment of time, the mean number of events observed during that increment is the number of events observed. It is known that radioactive decay follows a Poisson process. Therefore, the standard deviation of that observation is the square root of the mean - i.e. the square root of the number of observed counts. When we speak of the error in a measurement, we often are referring simply to the standard deviation of the distribution association with the variation in that measurement. If the distribution is a Poisson distribution then the error is the square root of the mean. If the distribution is gaussian then its error is given by the expression provided in table one. Often the relative error, sometimes called the fractional error, is quoted for a particular measurement. The relative error is simply the standard deviation divided by the mean. The Chi-Squared Test


A question which must be asked of any data is "Is the data random about the true value or are there systematic trends in the data?". A useful method of comparing two sets of data is the technique of comparing their variances. This is done by calculating a quantity called chi-squared:

The probability of a particular value of Χ2 as a function of the number of data points may be found in many reference books. A plot of Χ2 versus the number of data points is included in this laboratory write-up. In the plot provided the number of data points are expressed as the degrees of freedom. The degree of freedom in this case is the number of data points minus one. There are two different possible cases in regard to data stability. The spread in the data may be greater than predicted or the spread in the data may be too small indicating that it is not random. For example, one may calculate a value of Χ2 and then using the number of degrees of freedom correlate this to the probability (p) of this occurrence. If p < 0.02 the spread of the data indicates that the variation is greater than predicted and the data is being influenced by other extraneous factors. If p > 0.98, the data may be too good and it may not be random. This is just as bad as too large a spread in data. Generally, if the value of p is such that 0.10 < p < 0.90, then the data is considered to be random. A Chi-squared test should always be performed before starting an experiment to test the equipment. In addition, well designed experiments always include provisions to repeat one or more data points throughout the data recording period. An acceptable value of chi-squared determined from the repeated data points will determine if long term trends or systematic errors are present within the data set. Error Propagation The final result of measured data that is reported is usually the outcome of several concurrent measurements which are algebraically combined to produce the "final answer". An important question in this situation revolves around the value of error which should be reported. In order to determine the error in these situation one "propagates" the error

Χ2 = 1x

N

ji=1

(x _ xi)2


through the algebraic expression. The procedure for the propagation of error uses the following generalized expression: In this expression R, is the algebraic expression discussed above. R is a function of x1 and x2 and x3. The sigma values represent the error in each of the subscripted parameters which they represent. This particular form of the error propagation equation neglects a covariance term Normally, when performing radioanalysis of experimental data one does not encounter covariant variables. A good understanding of this procedure is necessary. It is a fundamental building block to many different ideas in experimental analysis.

PROCEDURE

1) With the G-M system that you have used during previous experiments take a series of 40 readings of a source, each for 1-minute.

A) Calculate the average of the data points and graph this as a solid horizontal line on linear graph paper. Label the x-axis simply 1 through 40.

B) Calculate the standard deviation of this data set and plot the value of the sum of the mean and this standard deviation as well as the difference of the mean and the standard deviation Plot these values as horizontal lines on your graph.

C) Repeat part B but employ the multiples of two and three sigma in this case. Your plot should have seven horizontal lines after it is completed.

D) Plot the 40 individual data points as "scatter" points on this graph. What fraction of these points lie within the mean plus or minus one sigma band on your graph? What fraction lie within the mean plus or minus two standard deviations on your graph? Are these fractions consistent with the preceding write up on statistics?

E) What is the fractional error (or relative error) of your data set?

F) Calculate the error of each data point and compare it to the error in the set of the data. Which is larger?

G) Determine the value of Chi-Squared for your data set. Is the detector operating properly?


2) Electronic timers may introduce counting errors when measuring counting rates. Hook up a pulse generator to count pulses at 10,000 cycles per second. Assume the frequency of the pulse generator is constant and accurate.

A) Make twenty 100-second measurements of the pulse generator data.

B) Determine the average and standard deviation of this data.

C) Calculate the value of CHI-squared from this data. Is this data random?

PROBLEMS (To hand in separately from Laboratory Report as homework) 1) An air sample was taken for 5 minutes """" 20 seconds. The air was sampled at a flow rate of 60 liter/minute """" 5 liters/minute. The sample was analyzed using a GM tube with an efficiency of 10%. During a 6000 second """" 200 second count time the system observed 5523 counts. An identical blank was counted for the exact same count time. The activity measured on the blank sample was 375 counts. What is the concentration of radioactive material sampled, be sure and report the appropriate propagated error in this sample.

Hint: In this case, R is given by the expression:

R = [(Counts) - (Background counts)]/[(efficiency)(air volume sampled)(count time)]

The air volume sampled is given by the expression: (flow rate) (sample time).

Show all of your work! Be sure to give the following information:

A) The concentration of radioactive material in the air. B) The error in this reported value. C) The relative error in this reported value. D) Which item produced the large portion of error in the overall expression?

APPENDIX

UNCERTAINTY ANALYSIS, STATISTICAL HYPOTHESES TESTI NG


I. INTRODUCTION

The goal of this appendix is to explain the rationale of uncertainly analysis and statistical hypotheses testing as it relates to nuclear counting. To achieve the goal a simple counting system will be considered. A simple counting system is considered to be a proportional counting system, a GM counting system, or a (high resolution) alpha counting system. This category does not include ionization chamber instruments.

Fundamentals of counting statistics are readily developed when considering a simple counting system. The results from the analysis of a simple counting system are used, by convention, as the basis for more complicated systems. It must be understood that these two kinds of systems, simple and complicated, present two entirely different sets of problems. Applying the results of a simple generalized counting system to a more complicated spectroscopy system is only done by convention as a way to standardize an approach to decision making.

II. FUNDAMENTAL CONCEPTS AND THE SIMPLE COUNTING SY STEM

A. Net Counts and Counting Uncertainty

The determination of net counts in the simple counting system involves only the subtraction of background counts away from the total counts;

NET = TOT - BKG

where:

TOT = Total Counts BKG = Background Counts

This calculation itself, and defining the terms for a simple counting system when performing paired observations is trivial. Since radioactive decay is best described as a Poisson process, the counts accumulated within a segment of time may be described with Poisson statistics. The standard deviation of a Poisson process is simply the square root of the number of events observed. Let us briefly consider the uncertainty or error in the value of total counts collected when using a simple counter.

In the case of a simple counter the following is true:


and the uncertainty or error of the background counts in this situation in which we are considering a simple counting system is:

To determine the uncertainty or error in the net counts, one must propagate the error of each of these values through the expression:

NET = TOT - BKG

Propagation of error is performed by evaluation of the following general

partial differential expression: This expression is used frequently. It is important for the student to understand its application. It can be used with any group of measurements when the measurement error is known. When used in this form, which ignores covariance, it is assumed that all sources of error are independent of each other. The following is an example of its application for the determination of Net Uncertainty.

Since NET = TOT - BKG then

of Total Counts=(Total Counts Collected)1ª2

of Background Counts=(Background Counts Collected)1ª2

=σBKG

[ ]Total 2=M

(Function,A.B.C...)

M(A)2 [ ] ofA 2 +

M(Function, A.B.C...)

M (B)2 [ ]B 2 +

M(Function,A.B.C...)

M (C)2 [ ]C .........

[ ]σNET2 =

M(TOT_BKG)

M(TOT)2 [ ]σTOT

2 +

M(TOT_BKG)

M(BKG)2 [ ]σBKG

2


Remember for a simple counting system where the background is obtained separately from the sample count the errors of the Total and Background are the square root of the number of counts collected. This type of counting procedure in which the sample's gross count and the background count are performed separately is known as a paired observation procedure. Carrying out the differentiation on the right side of the differential equation

given above results in the following expression:

A determination of net activity or concentration and their associated error terms from this point is simply a matter of applying the detector's efficiency, perhaps dead time correction, unit conversion, division by time, division by mass, or division by volume. It should be observed that counting uncertainty or error depends on the total number of counts recorded during a sample analysis. Often when people refer to counting error or counting uncertainty they are really trying to describe the coefficient of variation, which is synonymous with the percentage counting error or relative standard deviation. With reference to the context of the previous few paragraphs this ratio is:

Clearly, this is a useful concept. An evaluation of this shows one way to reduce analysis error. Since counting error depends on the total number of counts recorded, then the act of counting for a longer period of time, which allows more counts to be recorded, reduces the percentage counting error!

Because resources like time and counting equipment are limited, the investigator must choose a balance between analysis time and counting error. Figure 1 is a graph showing percentage counting error versus counting time. It is clear in Figure 1 that increasing counting time decreases percentage counting error. This is demonstrated by a sample counting both Co-60 and Cs-137 in very small quantities. One should not conclude that counting error can be reduced to zero. The reduction in percentage counting error for long

[ ]σNET2 =(1)2[ ]σTOT

2 + (_1)2[ ]σBKG2

[ ]σNET2 = [ ]σTOT

2 + [ ]σBKG2

Percentage Counting =σNET

NET X 100%


count times becomes asymptotic to the X-axis; zero error can never be achieved. It must also be pointed out that figure 1 is produced from one particular combination of detector, sources, and background. It is not a unique curve. Changing any one of the components of this combination will alter the shape of this curve somewhat.

B. Statistical Hypothesis Testing

After the values of the net count and its uncertainty are calculated it is necessary in many cases to determine if these values are above background, that is, if they represent an enhanced level of activity or not. This decision is made with the knowledge that the value calculated for the net count is only an estimate and that it can actually exist within a range of values. The position it actually has within this range is unknown but the probability of it falling at any location within the range may be described with reference to the estimated uncertainty calculated. Detection limit concepts arise from statistical hypothesis testing. The reason for such a test is to establish a uniform and rational framework by which a choice may be made between the Null Hypothesis:

HO: No net activity is present in the sample

And the alternate hypothesis:

H1: Net activity is present.

When a decision is made it is always possible that the decision was made in error. There are two types of errors which may arise under this circumstance. The first type of error, a type I or alpha error, is a false positive. The second type of error, a type II or beta error, is a false negative.

The following table elaborates on these types of errors.

(With reference to the presence of enhanced activity)

What We Conclude NO YES

What is Actually True NO Okay TYPE I YES TYPE II Okay


Frequently hypothesis tests of this type involve counting a sample and appropriate background. The number of net counts observed is used to decide whether net activity is present in the sample. We can create statistical decision rules which control the probability of making either type of error using this information.

The number LC is referred to as either the critical level or decision level. It is the decision rule used for controlling type I error. It is developed in a way so that the probability of making a type I error is a known value. Typically, this value is 5%. The decision made with this rule consequently would have a 95% probability of being correct and a 5% probability of being in error. If in error it is a type I error.

Using this decision rule, the Null Hypothesis is rejected in favor of the alternative hypothesis when the net counts exceed LC. To reiterate, this test criterion explicitly indicates a 95% confidence level. Adopting this test criterion creates a 5% risk of committing a Type I error. A type I error is a false positive detection. There is a 5% (as α = 0.05) probability that a background level sample will be discerned as having net activity. When considering a simple counting system the distribution of counts obtained from the background has a population mean µBKG and standard

deviation %%%%BKG. If the sample is at background level, the number of net counts that may be observed has a limiting mean µNET of 0 (µNET = 0) and

standard deviation of:

The term:

is obtained in the following way. Since NET = TOT - BKG, then as shown previously, the uncertainty in the net counts for a simple counting system is obtained from the expression:

σNET = ( BKG) ( 2) = ( BKG) (1.4142)

σNET = BKG . 2


Hence: Since in this case TOT = BKG, then Therefore

And If the distributions of interest are normal (which is an appropriate approximation if BKG $$$$50) (some say between 20 and 100), then the number LC has the following value:

The number 1.645 reflects the 95% confidence level of acceptance for a one tailed test. In principle, L C is determined by:

(1) The particular instrument (2) Its background (3) The counting time (4) Choice of the alpha level

LC is consequently an a priori (or before the fact) concept in regard to sample counting.

The second type of error which may be incurred in this context is that of false negative detection. This is the failure to detect net activity when in fact such activity is present in the sample. This is known as a Type II error. The probability (Β) of committing such an error clearly depends on the activity of

[ ]σNET2 =

M(TOT_BKG)

MTOT

2 [ ]σTOT2 +

M(TOT_BKG)

MBKG

2[ ]σBKG2

σNET2 = (+1)2σTOT2 + (_1)2 σBKG2

σBKG =σTOT = BKG

σNET2 = (1)σBKG2 + (1)σBKG2 = 2 σBKG2

σNET = ( 2) (σBKG)

LC=1.645 σNET = (1.645) 2. σBKG = 2.33 BKG


the sample. If the activity is quite elevated, there is very little likelihood that fewer than LC counts will be recorded. But this probability becomes high if the sample activity is only slightly above background. The detection limit LD is defined as follows:

LD is the number of mean net counts obtained from samples for which the observed net counts are 95% certain to exceed the critical level L C.

Under these conditions of counting a sample and a background, where the background approximates the sample in every way except radioactivity content, (a paired observation) it can be shown that L D is equal to

LD = 2.71 + 4.65 σBKG

This statement is developed as follows:

Let Kα = (1-α) PL

K β = (1-β) PL

where: PL = Probability Level, and when considering a one tailed test;

α = 0.05, Kα = 1.645 β = 0.05, Kβ = 1.645

To demonstrate how the expression for LD given above was developed,

consider the following definitions:

and Expressing LC in these terms yields:

[ ]σ02 = the variance when µNET = 0

[ ]σD2 = the variance when µNET = LD.

LC=2.33σBKG = 1.645 ( 2)σBKG = Kα( 2)σBKG = KσBKG = K

ασ0 .


Moreover when

It may also be seen that By definition

LD = LC + KβσD = LC + Kβ (LD + σ02 ) 2222

which is equivalent to

LD = LC + Kβ ( (%%%%L D) 2 + σ02 ) 2222

These two expressions are solved for LD as follows:

LD = LC + KβσD

LD = LC + Kβ (LD + σ02 )1/2

(LD - LC )2 = Kβ

2 LD + Kβ2 σ0

2

LD2 - 2LCLD + LC

2 = Kβ2 LD + Kβ

2 σ02

LD

2 - 2LCLD + LC2 - Kβ

2 LD - Kβ2 σ0

2 = 0

(σBKG)2 =µBKG

LC=Kασ0 = Kα(µBKG = ( BKG)2)1ª2

LC=Kα((σBKG)2 +σBKG2 )1ª2

LD_LC

Kβ

2=LD+σ02

(LD_LC)2

Kβ2 =LD+σ0

2


LD 2 - (2LC + Kβ

2 ) LD + LC 2 - Kβ

2 σ0 2 = 0

The solutions to this equation may be found by using the Quadratic Formula:

where a = 1 b = -(2LC + Kβ

2 ) c = LC 2 -Kβ

2 σ0 2

Thus the solution is: The portion of the expression influenced by the square root may be

simplified to:

which may in turn be simplified to:

Neglecting the negative sign of the """" term then yields: Rearranging this expression produces:

_b+_ [ ]b2_4ac 1ª2

2a

LD=2LC+K

2

β+_[(_(2LC+K

2

β))2_(4)(1)(L

2

C_K

2

βσ

2

0)]1ª2

2(1)

(2LC+K2

β)2_ 4(L

2

C_K

2

βσ

2

0)

4LCK2

β+K

4

β+4K

2

βσ

2

0

LD=LC+K2

β

2 +[4LCK

2

β+K

4

β+4K

2

βσ

20]1ª2

2


Factoring out Kβ4 from the radical produces the following expression:

Multiply by one in the form of

results in the expression:

We know that LC = Kασ0

Hence LC

2 = Kα2 σ0

2 and in the case where Kα = Kβ = K, this expression

then reduces to:

Since

LD=LC+K2

β

2

1+

1

K2

β

[4LCK2

β+K

4

β+4K

2

βσ

2

0] 1ª2

LD=LC+K2

β

2

1+

4LC

K2

β

+1+4σ

2

0

K2

β

1ª2

K2

α

K2

α

LD=LC+K2

β

2

1+

4LC

K2

β

+1+4σ2

0

K2

β

.K2

α

K2

α

1ª2

LD=LC+K2

2

1+

4LC

K2 +1+4L

2

C

K41ª2


is equivalent to the term in the bracket influenced by the square root, this statement may be written as

It can be seen that and then consequently

or at the 95% confidence level

This expression applies to a paired observation of a background and sample.

Analyses are often performed in situations where the background count time and sample count time are not equal. This is a special situation where the

2LC

K2 +1

2LC

K2 +1

LD=LC+K2

2

1+[2LCK2 +1]

LD=LC+K2

2

2+2LCK2

LD = LC+K2+LC = K

2+2LC

LD=K2+2LC=(1.645)

2+2(1.645( 2))(σBKG) = 2.71 + 4.65 σBKG .


decision rules developed for paired observation procedures must be modified slightly.

Consider a situation where two observations are made, one of a sample and one of a pure blank.

Let

S = true net signal B = true background e1 = the error in the observation of the signal and background e2 = the error in the observation of the background alone.

In this case the observed count Y1 is given as:

Y1 = S + B + e1

and the observed background is given as

Y2 = bB + e2

where b is the ratio of counting times:

b = blank/(blank + signal)

The net count in this set of observations would be given as:

Net = Y1 - Y2/b

Since error terms are incorporated within actual measurements the investigator must realize that the components e1 and e2 will always be present but implicit in the measurement taken. They are determined based on knowledge of the measurement process and knowledge of the phenomenon actually being measured.

Consequently, the error in the Net Counts is given as follows:


Under the null hypothesis the net counts are equal to zero, i.e., NET = 0 under this condition

reduces to;

It may be seen in this condition that:

when

It may be observed that η is a multiplier to convert σBKG to σNET.

Now consider a situation in which a sample is measured for time t1. Y1 counts are observed during this measurement. A blank is also measured which yields Y2 counts in a count time of t2. It is consistent with our discussion that t2 $$$$ t1 but this does not have to be the case.

σ2

net =

M(Y1 _ Y2ªb)MY1

2 [ ]σY1

2 +

M(Y1 _ Y2 ªb)MY2

2 [ ]σY2

2

σ2

NET = σY

1

2 + 1

b2 σY

2

2 $ Y1 +1

b2 Y2

σ2

NET $ Y1 +

1

b2 Y2

σ2

NET = B +

1

b2(bB) = B(1 +

1B)

σNET = σBKG η

η = 1 + 1b


The net counts measured in this sample may be obtained by the expression

where

b = t2/t1

This is analogous to subtracting the gross and background count rates (i.e.)

and then expressing the net counts obtained in the count time t1 as;

Previously it has been shown that:

since

NET = Y1 _ Y2

t1

t2 = Y1 _

Y2b

Net Rate = Y1t1 _

Y2t2 =

Y1 _ Y2

t1

t2t1

NET time t1 = Net Rate (t1) = Y1 _ Y2

t1

t2

LC = Kα σNET

σNET = σBKG [η]1ª2


it can be seen by substitution that

and therefore

substituting in b = t2/t1 this expression becomes;

and since B = Y2/b, this expression simplifies to:

LC = Kα σBKG (η)1ª2 = Kα(B η)1ª2

LC = KασBKG [1 + (1ªb) ] = Kα

B

1 +

1

b1ª2

LC = Kα[ ]Bη 1ª2 = Kα

B(t1 + t2)

t21ª2

as 1 + 1

(t2 ª t1)

= 1 + t1t2

= t2 + t1

t2

LC = Kα

Y2

t1

t2

(t1+t2)

t21ª2

LC = Kα

Y2

t1

t2

t1

t2 +

t2t2

1ª2


since R2 = Y2/t2 then

If we realize that the value for LC in this situation is actually a count rate, specifically the number of counts occurring in time t1 then the expression can be simplified to:

At the 95% confidence interval this becomes:

It should be noticed that LC in this expression represents the number of counts occurring in a specified time t1. It is interesting to observe that when t1=t2=t then:

Remember that for paired observation procedures, as performed using simple counting systems, LD is given by the expression:

LC = Kα

Y2

t21t22+Y2

t1t2t22

1ª2

LC = Kα

R2t

21

t2 +

R2t1t2t2

1ª2

LC = Kα

t1

R2

t2 +

R2t1

1ª2

LC = Kα

R2

t2 +

R2t1

1ª2

LC = 1.645

R2

t2 +

R2t1

1ª2

LC = 2.33

R2

t


The correct expression for LD in the special case where t2 …………t1 is found by substitution.

and at the 95% confidence interval where for a one tailed test K = 1.645:

when B = Y2/b $$$$ 70 the 2.71 may be dropped and an appropriate

approximation for L D becomes: It should be observed that in this special case LD is a count rate just as LC was pointed out as being a count rate under the same conditions.

LD = K2 + 2LC = K

2 + 2KσBKG

since, LC = K

R2

t2 +

R2t1

1ª2

then, LD =K2 + 2K

R2

t2 +

R2t1

1ª2

LD =(1.645)2 + 2(1.645)

R2

t2 +

R2t1

1ª2

LD = 2.71 + 3.29

R2

t2 +

R2t1

1ª2

LD $ 3.29

R2

t2 +

R2

t11ª2


These last expressions for LC and LD are numerically correct. They may, however, convey an incorrect notion that the reader must avoid. The error or uncertainty associated with a particular measurement is determined by applying Poisson statistics to an accumulated number of counts. This uncertainty is propagated through the manipulations of the data which result in an expression of count rate. It is not determined from the information about count rate.

The expressions developed for LC and LD for a simple counting system are a priori values based on the magnitude of background in a blank sample. The value of the expression LC, the critical level, is used in statistical hypothesis testing to verify the existence of a radionuclide in a sample a posteriori (after the fact). The LD value should be viewed as a parameter which cites the capabilities of a measured process under a given set of nominal experimental conditions.

The LD concept has great limitations in particular when applied to gamma spectroscopy. One limitation is that a change in the radionuclides present may drastically change the background and therefore invalidate what was calculated as LD. When describing this situation it is convenient to point out that background may be divided into two different categories. The first is that associated with the cosmic and terrestrial radiation bombarding the counting facility. This category also includes detector noise. The second is experienced from interference from other radiations within the sample to be analyzed. This second category is the reason why it is so very important to choose a background blank which approximates the sample as nearly as possible.

The second limitation is that the background under a peak in a gamma spectrum in not measured directly. The background area under a peak must be estimated. The error in the background in this case is the error propagated through the expression used to calculate background. The background component under a peak in a gamma spectrum and its error are estimates not direct measurements.

The LD concept is best used to compare different measurement processes or alternative implementations of a given well known processes or alternative implementations of a given well known process. It may also be used to determine if a proposed measurement method meets stated regulatory limits. It should not be used in a data base in lieu of an activity which could not be conclusively measured. This practice implies that although a material could not be identified, it exists in the samples at a value at least equal to that


maximum level which could be reasonably detected. This is a condition which has not been proven, and must be concluded as false.

Samples which reject the Null Hypothesis and accept the alternate hypothesis should be reported. Samples which do not cause rejection of the null hypothesis should cause the investigator to report the LD value. This must be clearly labeled. This does not imply that activity is present but only states the capabilities of the measurement process.

In some circumstances samples will cause rejection of the null hypothesis, their value will not exceed the value of LD, and they will usually have a large relative error. These values should be reported. Their quality may, however, be questionable. These are sometimes referred to as qualitative results versus higher activity samples which have clearly valid quantitative values. The value of such data sets must be understood by the user. Any level of rejection for this data would be arbitrary and cause some bias in data reporting. If the data is generated for a decision making process such value judgements may be necessary. Implicit in this issue is the question concerning a required action level. Such questions mut be weighted with many social and economic factors taken into consideration. The answer to these questions are usually not decide by the measuring laboratory.

Terms more commonly used than the LD level are the Minimum Detectable Activity (MDA) or Minimum Detectable Concentration (MDC). These play the same role conceptually as LD. They are the result of expressing LD in activity or concentration units. It is possible, however, that some of the quantities required to make these conversions may be subject to non-trivial uncertainty. When making such conversions the investigator should evaluate each term and propagate the error introduced by each term into the overall expression ultimately used. Certainly, all restrictions on use of LD also apply to its derivations: MDA and MDC.

Two other parameters exist which are also worth mentioning. One of these is the less than level or LTL. When no sample activity is present, the LTL is used to report the maximum amount of activity that may be present in the sample. Unlike MDA, LD, or MDC, the LTL level is not an a priori value. It may vary greatly between samples. It is particularly useful in high resolution gamma spectrometry where some net counts are identified within an energy range of interest but at values less than the critical level LC. Determination of the less than level counts is made using the following expression:


This expression is not frequently used because it is not universally accepted.

The second parameter worthy of mentioning is not particularly applicable to gamma spectrometry but may be appropriate when radiochemical treatments are required prior to spectrometric analysis. This parameter is the determination limit. The determination limit r eflects a minimum value which must be obtained in order to be confident of a specific precision (or relative standard deviation). In certain analyses it marks a boundary between qualitative and quantitative results. References: Detection Limit Concepts: Foundations, Myths, and Utilization. D.A. Chambless, S.S. DuBose, and E.L. Sensintabbar. Health Physics, September 1992, Vol. 63 number 3, pp. 338-340

Limits for Qualitative Detection and Quantitative Determination: Loyd A. Currie. Analytical Chemistry, March 1968, Vol. 40 number 3, pp. 586-593.

Application of Statistical Error Bounds to Detection Limits for Practical Counting: D. Mayer and L. Dauer, Health Physics, July 1993, Vol. 65 number 1, pp. 89 -91. (This article reviews the impact of systematic error on MDA/MDC estimates).

Accuracy and Detection Limits for Bioassay Measurements in Radiation Protection. *Statistical Considerations) NUREG-1156, 1986. A. Brodsky.

Gamma and X-ray Spectrometry with Semiconductor Detectors. Klaus Derbertin and Richard G. Helmer. Elsevier Science Publishers, 1988, pp 38-69.

Lower Limit of Detection: Definition and Elaboratio n of a Proposed Position for Radiological Effluent and Environmental Measurements. NUREG/CR-4007, 1984. L. A. Currie.

LTL(counts) = NET + 1.645 [ ]totalcount + (σBKG)2


GM-tube experiments

Half-life Backscatter

OBJECTIVE

1) Students will determine the half-life of an unknown radionuclide. 2) Students will perform experiments in which backscattering can be observed.

Introduction RADIOACTIVE DECAY The rate of transformation of a radionuclide, the rate of decay, is a first order reaction. The rate of decay is a function of the number of radioactive elements present in a sample. More formally, the rate of decay (dN/dt) is proportional to the total number N of atoms in

a radioactive sample: where:

dN/dt = the number of atoms decaying per unit of time, the rate of decay.

N = the total number of atoms present

It can be observed that the number of radioactive atoms decreases as time passes. With

this information we can make a specific statement: This is the instantaneous rate of decay at any time. The negative sign N decreases as the time increases. The variable λ is called the decay constant. The decay constant is a property of each radionuclide. The rate of decay is not altered by any known physical or chemical means. Neither pressure, temperature, chemical changes, gravitational fields, electrical fields, nor magnetic fields, effect the rate of decay. Radioactive decay is a RANDOM process. We can never determine when an individual

dNdt % N

dNdt = _λN


atom will decay. Given a population of atoms we can predict when a fraction of the population is likely to decay. Radioactive decay is a Poisson process. If we consider a population of atoms, and plot the number of atoms which decay in each finite increment of time following some initial starting point this plot will have a Poisson distribution. The rate of decay is actually used to describe the quantity of radioactive material present. We may call the rate of decay the activity (A) of the sample. The old unit of activity is the Curie (Ci). The new unit of activity is the becquerel. Originally the unit curie was based in the measured number of atoms disintegrating per unit time from one gram of Ra-226. This unit was named in honor of the Curies who discovered radium. Today, one curie is defined to be equal to 3.7x1010 disintegrations/second. Here we are using the word disintegration interchangeably with the word transformation. The SI unit of activity is the becquerel (Bq). A becquerel is one disintegration per second. There are 3.7x1010 Bq per 1.0 Ci.

1.0 Ci = 3.7x1010 Bq Alternately, we thinking about activity we may write:

This in itself is a useful expression, given any two variables in this equation we can determine the instantaneous value of the third variable. For instance, using this equation we can determine the instantaneous number of atoms present in a sample given the activity and the value of λ. The equation:

is a first order differential equation. We can solve this equation as follows:

First separate variables:

Then we integrate both sides of the equation:

A = dNdt = _λN

dNdt = _λN

dNN = _λdt


this result of this operation is:

where ln is the natural log function. lets allow Const2 - Const1 to equal ln(C), doing so allows the equation to be rewritten as:

We know, as an initial condition, that when time is equal to 0 (t = 0) the number of atoms can be assumed to equal N0, hence, this equation at time equals 0 becomes:

therefore; ln(No) = ln(C), or N0 = C. We can rewrite the equation as:

this is the same as: which is the same as:

rasing both sides by exp yields: This expression is sometimes called the exponential radioactive decay law.

∫dNN = ∫_λdt

ln(N) + Const1 = _λt + Const2

ln(N) = _λt + ln(C)

ln(N0) = 0 + ln(C)

ln(N) = _λt + ln(N0)

ln(N) _ ln(N0) = _λt

ln(NN0) = _λt

NN0 = exp_λt


Incidently, since A = -λN we may also write this as:

The number of disintegrations which have occurred over a period of time may be found by

integrating the expression:

from the beginning of the time of interest (t1)to the end of the time of interest (t2)as follows: We have already mentioned that the decay constant is a property of each radionuclide. There are several different way to describe the decay constant. Consider a plot of the ratio of A/Ao versus time. It can be observed that A/Ao decreases as a smooth function of time. This is the exponential decay function. If we look at any ratio of A/Ao and than at the ratio (0.5)(A/Ao) we can define the time it takes for one-half of atoms of a particular radionuclide to decay. This time is the radionuclide's half-life. Sometimes the half-life is called the physical half-life. The half-life can be used to describe the decay constant. Initially, we can state that in one half-life (t1/2) only one half of the activity we had initially (Ao) will be present. That is to say that the ratio of A/Ao will be 1/2. Under these conditions the exponential radioactive decay law can be written as:

taking the natural log of both sides of the equation produces:

AA0 = exp_λt

N0exp_λt

t2

∫t1

N0ext_λtdt = [

N0_λ

exp_λt

t2

]t1

12 = exp

_λt1ª2

ln(12) = _λt1ª2


this is equal to:

consequently: This is one definition of the decay constant. The half-life of a radionuclide is commonly found in the literature. Several sources include:

The Chart of the Nuclides The Health Physics and Radiological Health Handbook The CRC Handbook of Chemistry and Physics The Radiological Health Handbook (of 1970)

Another methods of describing the decay constant is sometimes also encountered. This is the average or mean life (τ): The average or mean life is the reciprocal of the decay constant (i.e)

τ = 1/λ. Hypothetically, one could speak of the tenth-life or fifth-life or any other such thing. Such a parameter would be defined similarly to the half-life parameter. It is interesting to point out two items when discussing the exponential radioactive decay law and the half-life. First since the exponential decay law describes exponential decay and since exponential functions never reaches zero items which are radioactive will always be radioactive theoretically. That being said what does it mean. It means that if we had billions and billions of radioactive atoms we can not predict when any particular atom in the population will decay. Hence we can not predict when the very last atom in that population will decay. The exponential function is asymptotic to the zero value. The expression exp-λt can be thought of as the probability of a number of atoms decaying within a certain period of time. As t gets large this probability becomes very small. As a rule of thumb we say that after the tenth half-life a radioactive material is considered to decay away "completely". This obviously applies when dealing with medium to small sources of radioactivity. For very large sources of radioactivity even after the tenth half-

_0.693 = _λt1ª2

λ = 0.693

t1ª2


life there may still be a considerable amount of radioactive material present relatively speaking. A second interesting item is an argument: Some argue that every atom in the universe is in reality radioactive. What we refer to as stable species simply have half-lives which are so long that we can not measure them. Students are encouraged to think about this idea for a while. Half-life values for radionuclides range from fractions of a (i.e 10-13 s) second to billions of years (i.e. 2x1018 y - Bi-209). BACKSCATTERING Radiation is emitted from a source in all directions. If the radiation is emitted in the direction of the detector, and if it enters the detector chamber, there is a good chance it will be detected. Radiation emitted in other directions will not usually be counted. When radiation interacts with matter it is sometimes deflected or scattered into a new direction. This is particularly true of beta radiation. During such an event the radiation may be either absorbed or scattered. Typically, several collisions occur scattering the particle about in many different directions. These occur in a very small increment of time. These collisions may be elastic or inelastic. When considering charged particles these are by and large coulombic interactions. Most charged particle interactions are inelastic. The result of these collisions is not only a change in direction but also a small loss in particle energy. Often the source-detector system contains more than just the source and the detector. One expects to find structural material surrounding both the source and the detector. This may include for instance the source backing and the shelf which supports the source in a reproducible geometry. Sometimes radiation interacts with these components. It is possible that the scattered radiation is scattered back into the detector. This occurs even though the initial direction of the radiation emitted from the source was away from the detector. Radiation which is scattered through an angle of nearly 180EEEE is said to be back scattered. The phenomenon of radiation scattering into the detector is known as backscattering. The effect of backscattering is an increase in the observed count rate over what is expected from geometrical considerations alone.

PROCEDURE

1) Determination of a samples half-life.


a) Set up the G-M detector as indicated by previous experimentation.

b) Obtain a standard source from the instructor and count this source in a specific position relative to the detector for 10 minutes. Count a "blank sample" in this geometry for ten minutes. Also count the "unknown" sample - placed in this same geometry for ten minutes.

c) Repeat this procedure at the intervals specified by the laboratory instructor.

Note: this sample may need to be count on different days over a period of a week. d) Correcting all data for resolving time errors, background, and normalizing based on the standard source counts on the first day, develop a table of time versus true count rate.

e) Perform a least squares fit of this data. The slope of this line corresponds to the half-life of the sample.

f) Plot this data on "natural" semi-log paper. Alternately, one may plot the natural log transformed counts on linear-linear paper. The time required for the half-life to decrease by a factor of 2 corresponds to the half-life of the unknown.

g) Report the half-life determined experimentally.

2) Backscattering

a) Handling the source with tweezers, count the beta source provided for 5 minutes. Do not touch the source with your fingers. After class be sure to frisk your fingers before leaving.

b) Place one of the metal foils provided behind the source and recount the source.

c) Repeat this procedure several times adding a another thickness of foil each time. Keep the face of the source in the same position relative to the detector each time.

d) Plot the number of counts observed on the Y-axis versus the thickness of metal behind the source e) Repeat this procedure using a different type of metal foil. Plot the data


from this series of experiments on the plot developed above.

Proportional Counters OBJECTIVES:

1) The student will determine the operational plateau for a proportional counter by graphing the observed counts/second from a radiation source as a function of applied voltage.

2) This operational plateau will be used to discriminate between alpha and beta radiation emitted from an unidentified radionuclide.

DISCUSSION: Gas filled radiation detection systems depend upon the products of the interaction of ionizing radiation with the gas contained in the detector. After an ionization event, the detector's fill gas will contain positive ions and free electrons. The behavior of these charged particles will depend on the magnitude of the electric field within the detector's sensitive volume. If there is no electric field, the ions will recombine. When a slight electrical field is encountered the charged particles will begin to migrate toward the appropriate electrodes associated with this field. Some of the electrons will reach the anode, perhaps a few of the positive ions will reach the cathode. The higher the applied voltage, the faster the charged particles move. As the applied voltage increases, more and more ions will be collected at their respective electrodes. After a certain voltage is attained, all of the ions generated by the incident radiation are collected. As more potential is applied across the anode and cathode gas multiplication is observed. Gas multiplication as the name implies, is the production of more ion pairs in the fill gas than were created by the incident radiation. Gas multiplication is the result of collisions between the rapidly moving charged particles and other molecules of gas within the detector's sensitive region. Depending on the kinetic energy of the charged particles moving under the influence of the applied electric field, these collision may result in either further ionization or excitations. The charged particles caused by ionization in this situation behave just as those created by the incident radiation. The excited molecules will de-excite usually producing UV-light photons. The UV-light photons may under some circumstances cause further ionization of those molecules within the strong electrical fields existing between the detector's anode and cathode. A plot of the number of ions collected at the electrode with respect to the applied voltage is shown in figure 1. Figure 1 illustrates the experiences of charged particles within gas filled detectors. The first region of this figure is called the recombination region. In this region, the voltage is insufficient to collect all ions produced. Thus, these ions may simply recombine.


In the second region, referred to as the ionization region, the electric field is sufficiently large to "sweep" all of the ions to their respective electrodes. All of the ions generated by the incident radiation are collected. With increasing electric field strength, accelerated ions can gain enough energy to ionize the atoms with which they collide. In this fashion, as mentioned above, a multiplication of ions takes place. The applied voltage at which gas multiplication just starts determines the end of the ionization region and the beginning of the proportional region (corresponding to region 3 in figure 1). In this region, the number of ions collected on electrodes of the detector is greater than initially produced by incident radiation. The number of ions collected is linearly proportional to the energy deposited by the incident radiation. More ions will be collected from an incident alpha radiation than an incident beta radiation.

Figure 1.


Gas multiplication is observed within the proportional region. In the proportional region gas multiplication occurs in a linear fashion with increasing voltage. As a charged particle is accelerated through the electric field, it is likely that collisions will occur between it and the neutral gas molecules contained within the electric field. These secondary particles can cause both ionization and excitation. Such collisions, causing both ionization and excitation, can result in the production of additional charged particles which will also be accelerated by the electric field. This phenomena is known as gas multiplication. Gas multiplication takes the form of a cascade, or Townsend avalanche, during which free electrons may create additional free electrons as these migrating electrons collide with gas molecules. As the potential between the anode and cathode is increased further, gas multiplication losses its linearity. Every incremental increase in voltage produces more than a linear increase in the number of ions collected. The region of figure 1 in which this occurs is called the limited proportional region. This region is not useful for radioanalysis work. The gas multiplication experienced with greater increases in the applied voltage is so large that the detector becomes saturated with ions. Every incident radiation, regardless of type, causes a complete collapse of the electric field. A strong signal pulse is produced with every event. This pulse is always of the same magnitude and its size is independent of the type of incident radiation. Know information about the energy of the incident radiation is available. However, because of the large signal pulse gas filled detectors operated in this region, the GM region, are considered to be fairly sensitive. If the potential applied between the electrodes of a gas filled detector is increased even further the detector begins to saturate and remain saturated. Under many circumstances maintaining a potential at this extreme will damage the detector, particularly if it is a sealed system with a limited quantity of fill gas. This region is referred to as the region of continuous discharge. SPECIFICS ON PROPORTIONAL COUNTERS Radiation detectors (counters) for which the total number of ions produced is proportional to the energy of the radiation are referred to as proportional counters. The design of proportional counters vary depending upon the type of the radiation being detected. A typical design for a proportional counters employees a cylindrical electrode and a central wire (refer to figure 2). This particular design is a good one to emphasis variation in the strength of the electric field over the active region of the detector.


Figure 2 Due to the geometry of this device, the resulting electric field at a distance x from the wire is given as:

E = V/{x ln(a/b)} Equation 1

where:

V = applied voltage between electrodes a = radii of the outer electrode b = radii of central electrode x = the distance between the central wire and point in question.

If we study this equation, we notice that the electric field is larger near the wire and that it decreases as the distance from the wire increases. Hence, most multiplication takes place near the central wire. Since electrons are produced near the central electrode, the change in potential at the central electrode (due to collection of these electrons) is small. The resulting pulse has a very short rise time and a slower decay time. Ionization is limited to a region surrounding the path of the radiation in proportional counters. It is likely, that multiple ionization events may take place in an individual counter due the volume of gas involved. Often, there will not be adequate time between events to allow the potential to return to zero. Assume for example that radiation 1 enters the gas volume at time t1 and that another radiation enters at time t2. The drop in potential at the collecting electrode will resemble that in Figure 3. As a function of time.


Figure 3. If the NIM counting equipment can distinguish the voltage change for the two pulses and the minimum time separation between these two pulses, then the resolving time for the proportional counter is t2 - t1. Hence, the resolving time for a proportional counting system is dependent upon the electrical system used. The proportional counter used in this lab experiment is a gas flow counter with a thin window. These are commonly used to discriminate between alpha and beta particles. In this case, the fill gas can be directly and continuously introduced into the counter. In the proportional region in figure 1, note that two distinct plots exist. The upper line corresponds to a larger number of ions being collected at a specific voltage. Alpha radiations tend to produce larger pulses than beta radiations at the same applied voltage, it can be concluded that a greater number of alpha counts will be obtained compared to the number of beta counts during the same time interval with the same applied voltage. One of the objectives of this lab is to graph the characteristic curve of counts/sec as a function of voltage (similar to what is shown in figure 4). This will be done for a single source which emits alpha particles as well as beta particles. Such curves take advantage of the different ionizing properties of the different radiations and a linear responding gas amplification factor. The pulse heights produced by alpha particles are greater than those produced by beta particles. Therefore, alpha particles will be counted at the lower voltages where beta particles will be "intrinsically" discri minated. At such a low voltage the relatively small pulse produced by a beta particle will not be large enough to be distinguished from noise. As voltage increases, beta pulses become sufficiently large to be counted along with the alpha particles. This results in the two distinct plateaus as shown in Figure 4.


Figure 4 PROCEDURE: Determination of operating plateau

1. Set up proportional counter and NIM equipment as explained by the lab instructor. Be sure to have the lab instructor check to insure that the proportional counter, gas-flow, and supporting electronic equipment is set up safely and properly before initiating experiment. Sketch the set up used and include a wiring diagram of the electronic equipment used.

2. Obtain alpha/beta source and place the source on the appropriate shelf of the detector as directed by the lab instructor. Record the type of source and its activity. Refer to the Chart of Nuclides and determine the energy, frequency of alpha and beta emissions, as well as the half-life of the radionuclide.

3. Set the High Voltage Supply at 100 V and count sample for 1 minute. Record the number of counts.

4. After counting for 1 minute, increase voltage by 100 V and repeat step 3. Repeat this process until a noticeable count rate is experienced after a second plateau is observed.

5. Plot a graph of the Counting rate vs. Voltage for each data point obtained in the preceding procedure. Identify the different plateaus on the resulting graph.

6. Repeat steps 1 through 5 using a different alpha/beta source. Record the type of


source and its activity. Use the chart of the Nuclides to determine the energy, frequency of alpha and beta emissions, and half-life of radionuclide. Plot the operational plateau on a separate graph (of the same size) but use the same graduations as on the previous plot of the operational plateau.

References: Knoll, Glenn F. Radiation Detection and Measurement. 2nd ed. New York: John Wiley & Sons; 1989. Ouseph, P. J. Introduction to Nuclear Radiation Detectors. New York: Plenum Press; 1975. Turner, James E. Atoms, Radiation, and Radiation Protection. New York: McGraw-Hill; 1992.


Environmental Monitoring OBJECTIVES:

1) The purpose of laboratory experiment is to gain an understanding and an appreciation of the methodology used for Environmental Air Monitoring.

2) Another purpose of this investigation is to elaborate on the students understanding of the differences between a radiation field, and radioactive contamination. Students will perform swipe samples and distinguish between long lived and short lived radionuclides on the samples.

3) As a third objective the student will learn how to determine the activity and air concentration of an individual environmental air sample.

4) Methods for determining gross alpha and beta activity will be experienced by the student. Students will determine values of LD, LC and MDA for their detector systems and employ them during sample analysis.

DISCUSSION:

Environmental air monitoring is performed by first collecting air samples and then determining the activity of radioactive material present on the sample media. Generally, the radioactive components found in air are difficult to monitor using standard portable survey equipment due to the lack on instrument sensitivity. Air samples are collected and then measured for activity using more sensitive laboratory detector systems (e.g. NaI(Tl) scintillation counters, gas-flow proportional counters, high resolution semi-conductor detectors. etc.).

One may in general terms describe air sampling techniques in two categories, passive sampling and active sampling. The passive collection of potential air contaminants employs either sample media with a large surface area such as activated charcoal or as an alternate a sampling system that incorporates a semi-permeable membrane. Both systems develop a localized concentration gradient motivating the collection of radioactive gases by diffusion. Active sampling requires a mechanical means of pulling a volume of air pastor through the collection media. Typically a vacuum pump is employed to move the sampled volume of air through the sampling media. Such systems are frequently referred to as grab sampling systems particularly if the sampling time is short. When the sampling time is long stretching into hours or weeks the sampling system may more appropriately be referred to as a continuous sampling system.


The most common radioactive air contaminant is Radon-222 (referred to as radon). Radon is a naturally occurring radionuclide. By far radon and its short lived alpha emitting progeny are responsible for the largest fraction of background radiation dose experienced by most people. The dose delivered by radon and is progeny is primarily a dose directly to the lung. The element radon itself is an inert gas. It happens that radon itself is not responsible for a very large fraction of the dose delivered to lung tissue. Radon gas is inhaled and as readily exhaled. The radon progeny, however, are typically charged particles. These adhere to small particles always present in the air. These small particles are inhaled and deposited within the lung structure. The trapped radon progeny decay releasing their energetic radiation particles (most importantly alpha particl es) in to the living lung tissue producing the maximum biological effect. Radon is considered to be a major public health problem due to the build-up of radon and radon progeny in homes AAAAsealed@@@@ for the purpose of energy conservation. Have you had the levels of radon and radon progeny in your house evaluated?

There are several ways to monitor the concentration of radon and its progeny in air. Commonly activated charcoal is used to collect air samples suspected of containing detectable amounts of radon gas. Activated charcoal has a large affinity for many different types of gases and vapors including radon because of its extraordinarily large surface area. Radon is adsorbed onto the activated charcoal grains. The radon then undergoes radioactive decay which producing the progeny polonium-218, lead-214, bismuth-214, polonium-214, lead-210, and others. Radon concentrations can be determined by counting alpha emissions of the radon or by counting the gamma ray emissions of both the lead-214 (295 and 352 keV) and bismuth-214 (609 keV). Determination of radon concentrations through gamma counting is possible due to the relatively short half-lives of these progeny. Within three hours, the progeny are in equilibrium with radon.

To insure accuracy in determination of radon air concentrations, performance of the counting systems used must be determined by counting standard canisters (which contain known radioactivity) and background canisters. These canisters should be counted daily to establish a daily counting efficiency for each detector system. This is referred to as the systems relative efficiency and applies to the particular geometry of the standard exclusively. Typically the counting efficiency is determined by counting the standard and background canisters each for ten minutes. The background count is subtracted from the standard count to obtain a net count. This is then divided by the time (10 minutes) to obtain net counts per minute (CPM). By dividing the net CPM by the known activity of the standard, the standard efficiency (CPM/pCi) of the detector for that day is determined.

Since activated charcoal has an affinity for water vapor, humidity will influence the


charcoal canisters ability to collect radon. Corrections must be made to account for the influence of water on counting efficiency. Such corrections are determined through the determination of a calibration factor. A calibration factor is calculated for each charcoal canister using the following equation:

CF = Net CPM (Equation 1) (Ts)(E)(Rn)(DF)

where,

CF = Calibration factor, radon adsorption rate (l/min) Net CPM = Gross CPM for that canister - Background CPM for that

detector for that day

Ts = Exposure time of the canister (minutes) E = Detector efficiency for the appropriate detector (CPM/pCi) Rn = Radon concentration in the chamber for the exposure period (pCi/l) DF = Decay factor from the midpoint of exposure to the time of counting

from the equation:

DF = exp(-.693t/5501 minutes)

where, t = time in minutes from midpoint of exposure to the start of counting.

5501 minutes corresponds to the radioactive half-life of radon in minutes.

These calibration factors are used to generate two tables and two curves. Table 1 relates calibration factor to water weight gain for the canisters for a 2 day exposure. This data is used to plot figure 1. Table 2 relates exposure time to adjusting factors for 20, 50, and 80 percent humidity. Data in this table is plotted in figure 2.

Water Gain vs. Calibration Factors For a 2 Day Exposure of activated charcoal to ambient room conditions.


Table 1.

Percent Humidity Water gain (g) C.F. (l/min) 20 0 0.101 20 0 0.105 20 0 0.11 20 0 0.107 50 1.7 0.098 50 1.8 0.094 50 1.9 0.097 50 1.8 0.102 50 1.8 0.096 80 7.7 0.077 80 7.5 0.082 80 7.7 0.076 80 7.9 0.076 80 7.9 0.078

Table 2.

"Exposure Time vs. Adjustment Factors for Low, Medium, and High Humidity" Time of Exposure Adjustment Factors (l/min) (Hours) 20 percent 50 percent 80 percent 24 0.137 0.132 0.116 24 0.143 0.137 0.125 24 0.141 0.132 0.118 24 0.135 0.126 0.117 24 0.138 0.127 0.118 48 0.107 0.096 0.077 48 0.110 0.102 0.082 48 0.105 0.097 0.076 48 0.101 0.094 0.076 48 0.105 0.098 0.078 72 0.087 0.075 0.048 72 0.091 0.079 0.051 72 0.088 0.075 0.051 72 0.083 0.073 0.046 72 0.085 0.075 0.049 96 0.074 0.058 0.035 96 0.080 0.062 0.034 96 0.075 0.059 0.033 96 0.074 0.057 0.033 96 0.075 0.060 0.034 120 0.070 0.051 0.023 120 0.073 0.054 0.025 120 0.071 0.051 0.024 120 0.069 0.050 0.023 120 0.071 0.052 0.023 144 0.064 0.045 0.018 144 0.068 0.047 0.019 144 0.064 0.047 0.016 144 0.062 0.047 0.018


Figure 1


Figure 2


Equation 1 may be rearranged to solve for the radon concentration if the calibration factor is known:

Rn = Net CPM (Equation 2)

(Ts)(E)(CF)(DF)

where, Rn = Radon concentration in pCi/l Net CPM = Gross CPM for canister - background CPM

for that detector that day Ts = Canister exposure time (minutes) E = Detector efficiency (CPM/pCi) CF = Calibration factor from tables DF = Decay factor from the midpoint of exposure to the start of

counting

Gas-Flow proportional counters can be used in conjunction with either activated charcoal filters or grab sample filters. A problem which may arise in determination of radon air concentrations and activity is due to the production of radioactive progeny. To determine the radon concentration in air by counting the gamma emission from radon progeny, it is necessary to allow the radon to decay to a state of equilibrium with its radioactive progeny being counted. This generally takes 4 to 5 days. Another method to determine the concentration of radon in air takes 24 hours.

The KOVAL Method is used to quickly analyze environmental samples without having to wait for the decay of radon/thoron daughters. The Koval Method takes advantage of known decay curves of natural radioactivity to determine the activity of man-made radioactivity found in the sample. Figure 3 demonstrates the activity of a given sample as a function of time. Note, the total observed count rate is dependent upon the decay of radon and thoron daughters in addition to the activity resulting from man-made sources which may be found in the sample. Due to the relatively short half-lives involved, two sample counts are required. One sample count is performed at t = 4 hours and a second sample count at t = 24 hours. This can be represented by the following expressions:

A4Total = A4

Natural + A4Manmade

and A24

Total = A24Natural + A24

Manmade


where,

A4Total = total activity at t = 4 hours

A4

Natural = natural activity at t = 4 hours

A4Manmade = man-made activity at t = 4 hours

A24

Total = total activity at t = 24 hours

A24Natural = natural activity at t = 24 hours

A24

Manmade = man-made activity at t = 24 hours Since the man-made component has a relatively longer half-life than that of the natural component, it can be assumed that

A4Manmade = A24

Manmade Of the natural component, 212Pb has the longest half-life of 10.6 hours. So,

A24Natural = A4

Natural exp[{-0.693(20)}/10.6]

A24Natural = A4

Natural(0.27) By substitution,

A4Total = A4

Natural + AManmade

A24Total = A4

Natural(0.27) + AManmade

A4Total - AManmade = (A24

Total - AManmade)/0.27

A4Total - AManmade + AManmade/0.27 = A24

Total/0.27

(AManmade/0.27) - AManmade = (A24Total/0.27) - A4

Total

AManmade(1/0.27 - 1) = (A24Total/0.27) - A4

Total

AManmade(2.7) = (A24Total/0.27) - A4

Total

AManmade = 1.37A24Total - 0.37A4

Total


Dry-Lab Procedure

1. A Radon sample was collected using an activated charcoal sampler. The following parameters were obtained:

Initial mass of cartridge = 158.7 g Final mass of cartridge = 158.8 g Exposure period: 2/17/95 at 0830 MST to 2/19/95 at 0900 MST Gross counts = 3013 in 10 minutes Background counts = 668 in 10 minutes Standard counts = 60,211 in 10 minutes for 20.5 microcurie source

Determine the radon concentration (pCi/l) in air and determine counting error within 95% confidence interval.

2. A grab sampler used to collect an air sample depends upon a vacuum pump to draw air through a filter. The sampler used for the following environmental sample has a capacity to draw 0.1 cubic feet per minute through the filter for a 12 hour period. The sample was then counted with a gas flow proportional counter. The sample was counted at five different times for ten minutes. A 2.4 microcurie Radium-226 standard was counted to determine detector efficiency and to normalize the sample counts. The data was recorded in the following table:

Sample Total Counts (10 minutes)

Counting Counting Environmental Date Time (MST) Sample Sample Background 2/19/95 4:10 PM 3292145 2664001 1701 2/19/95 8:00 PM 3199961 2659998 1677 2/20/95 8:05 AM 3012150 2663997 1602 2/20/95 12:15 PM 2954259 2673201 1597 2/20/95 4:30 PM 2898098 2751995 1822 2/20/95 7:55 PM 2843679 2659989 1756

a. Calculate net count rate (counts per minute). Plot the sample counts as a function of time. Include counting error in the graph.

b. Considering detector efficiency and the plot of count rate as a function of time, determine the activities of the two primary radionuclides found in the sample.


c. Determine the half-lives of the radionuclides detected and estimate the identity of radionuclides.

d. Estimate the air concentrations (in pCi/L) of the radionuclides counted.

Lab Procedure:

1. Set up the gas flow proportional counters as accomplished during the last laboratory session.

A) Rapidly verify that the operating plateaus developed during the last laboratory session are still valid.

2. Using the air sampling systems provided in the laboratory obtain a 20-minute air grab sample using a paper filter collection media. Make sure you note the volumetric flow rate being pulled through the sample.

A) Analysis the activity of gross alpha and beta activity on that sample.

a. Be sure to make efficiency corrections B) Determine the concentration of gross alpha and beta radioactivity in the air sample obtained. C) Analysis the sample several times over the following 24-hours and use the KOVAL method to distinguish if long-lived radioactive material is present in the sample. D) Determine the analysis capabilities of your proportional counting system.

a. Calculate the LC, LD, and MDA. Is the activity you measured actually detectable using the counting systems employed?

3. Obtain a AAAAswipe@@@@ sample from the face of a dusty CRT screen and perform an analysis of this for the presence of gross alpha and beta radiation emission. Report the activity in units of pCi/100cm2.

4. 5 points extra-credit for undergraduates and required for graduates students. Organize into sub-groups and setup a gross alpha and beta gas flow proportional counting system that employs a AAAAguard-ring @@@@ active background removal detector and which performs simultaneous alpha-beta analysis using standard NIM equipment. Note this activity may require some out-of-class time.


QUESTIONS: (To be handed in separately from Laboratory report as homework to replace one laboratory quiz grade)

1. What factors influence the efficiency of sample collection?

2. Outline a method in which a gas-flow proportional counter could be used to identify multiple (<2) radionuclides found in an environmental sample.

3. Can the Koval method be used to determine the activity of an unknown sample which has a half-life of the same order of magnitude as the short-lived naturally occurring radionuclides? Explain.

4. What assumptions must be made in order to determine radionuclide concentrations?


HANDLING PROCEDURE FOR SHEPHERD CS-137 IRRADIATOR (S/N 28-6A)

1. Pre-use Handling Precautions

1.1 Obtain RSO permission to use the Shepherd source. 1.2 Ensure personnel in the 1 mrem/hr boundary of the source have a pocket

dosimeter. 1.3 If the electronic dosimeter is available one person should have it on his person. 1.4 Perform an initial radiation survey. Ensure that survey meter has been

calibrated within the last six months. Exposure rate at any point on the surface should not exceed 10 mr/hr.

1.5 Check that the lock is in place and locked. 1.6 Conduct a visual inspection of the irradiator. Check for any physical damage. 1.7 Move the irradiator to a use location approved by the RSO.

2. Exposing the Source.

2.1 Place rope barriers and "Radiation Area" at the (source exposed) 1 mrem/hr boundaries. Use of locked doors is an acceptable alternative to rope boundaries.

2.2 Check, again, that all personnel involved with the source exposure have proper dosimetry.

2.3 Unlock the source. WHILE THE IRRADIATOR IS UNLO CKED, BOTH IT AND THE AREA WITHIN THE 1 MR/HR BOUNDARY WILL BE KE PT UNDER SURVEILLANCE AT ALL TIMES.

2.4 Expose the source and verify operation of the warning lights and the 1 mrem boundaries. House the source.

2.5 Perform the required calibration procedure with the Shepherd irradiator. 2.6 If at any time the source becomes stuck in the exposed position, or if an

unacceptably high exposure is believed to be received, inform the RSO at 3669. 2.7 Lock the source. Survey as in 1.4 above


3. Post Exposure

3.1 Return the irradiator to it's storage location. 3.2 Perform a radiation survey of the Shepherd source once it is in storage location. 3.3 Inform the RSO of the status of the source.

EXPOSURE RATE VALUES FOR SHEPHERD ONE CURIE CESIUM-137 BEAM IRRADIATOR, SERIAL NUMBER 587

Based on the original calibration and the subsequent calibration checks and determinations of attenuation factors, the following expression can be used for the exposure rate in mR h-1 for the irradiator.

The values of AF for the attenuators are as follows:

1B (1.8 cm lead) 0.100

1A (3.7 cm lead) 0.0114 If no attenuator is used, the value of AF is 1.00.

X=309.4HAFHe-0.0231H t

r2


IDAHO STATE UNIVERSITY TECHNICAL SAFETY OFFICE MEMO DATE: December 11, 1991 TO: Radiation Protection Files FROM: Tom Gesell SUBJECT: Check of the primary calibration of Shepherd Model 28 "one curie" 137Cs

Irradiator, serial number 587. This memorandum to file documents a check of the calibration of the subject irradiator. The measurements were performed from 1700 to 1900 hours on 11/19/91 in the basement of the College of Engineering using the same geometry as for instrument calibration. The primary calibration of the subject irradiator was checked by separately measuring the exposure over a period of approximately 20 minutes with two 250 mR Victoreen Model 570 Condenser R-meter chambers at a distance of 1.00 meters from the source in essentially free air conditions. The R-meter measurements were made in accordance with the attached instruction manual. Exposure time, distance and temperature measurements were made with normal commercial devices which were not subjected to any special calibration. Absolute atmospheric pressure was obtained by telephone from the Pocatello NOAA office at 1700 hours. The R-meter and associated chambers were calibrated directly by NBS (now NIST). A copy of the NBS calibration certificate is attached. The exposure

rates (X dot) were calculated in accordance with equations 1 and 2 below.

FN =

273.15+T

295.15 H760P

X = SRHFNHCF

tX


MEMO Check of the primary calibration of ... 12/11/91 (continued) The original calibration certificate supplied with the irradiator indicated an exposure rate of 421 mR h-1 on August 31, 1978. The elapsed time between August 31, 1978 and the date of calibration, November 19.1991 is 13 years and 80 days or 13.22 years. The half life of 137Cs was taken as 30.0 years. Using the standard radioactive decay formula, the fraction of the activity remaining on the calibration date is 0.737. Thus the expected exposure rate is 421 X 0.737 = 310 mR h-1. The pertinent data and results are listed below. ITEM CHAMBER # X1246 CHAMBER #88 Pressure (P) 649 mm Hg 649 mm Hg Temperature (T) 23.3 oC 23.3 oC Scale Reading (SR) 82 units 85 units Normalization Factor 1.176 1.176 Exposure Time (tX) 0.338 h 0.333 h NBS (NIST) Correction Factor 1.06 1.06 Measured Exposure Rate 302 mR h-1 318 mR h-1 Average Measured Exposure Rate 310 mR h-1 Expected Exposure Rate 310 mR h-1 The average measured exposure rate and the expected exposure rate calculated from the calibration certificate supplied with the irradiato r are identical to three significant figures. This high degree of agreement is certainly fortuitous. An agreement to within 5% would be good and agreement to within 10% would be acceptable. Attachments: Victoreen Model 570 R-meter Instruction Manual (copy)

NBS (NIST) Calibration Certificate (copy) Shepherd Irradiator Calibration Certificate (copy)

cc: Bernie Graham, w/o attachments


IDAHO STATE UNIVERSITY TECHNICAL SAFETY OFFICE MEMO DATE: December 11, 1991 TO: Radiation Protection Files FROM: Tom Gesell SUBJECT: Approximate check of the calibration of Shepherd Model 28 "one curie" 137Cs

Irradiator, serial number 587 with the thin lead attenuator. This memorandum to file documents an approximate check of the calibration of the subject irradiator. The measurements were performed from 1700 to 1900 hours on 11/19/91 in the basement of the College of Engineering using the same geometry as for instrument calibration. The calibration of the subject irradiator with the thin lead attenuator was checked by measuring the exposure over a period of 21.5 minutes with a 25 mR Victoreen Model 570 Condenser R-meter chambers at a distance of 1.00 meters from the source in essentially free air conditions. The R-meter measurement was made in accordance with the attached instruction manual. Exposure time, distance and temperature measurements were made with normal commercial devices which were not subjected to any special calibration. Absolute atmospheric pressure was obtained by telephone from the Pocatello NOAA office at 1700 hours. The R-meter and associated chambers were calibrated directly by NBS (now NIST). A copy of the NBS calibration certificate is attached. The exposure rates (X dot) were calculated in accordance with equations 1 and 2 below.

FN =

273.15+T

295.15 H760P

X = SRHFNHCF

tX


MEMO Check of the primary calibration of ... 12/11/91 (continued) The original calibration certificate supplied with the irradiator indicated an exposure rate of 421 mR h-1 on August 31, 1978. The elapsed time between August 31, 1978 and the date of calibration, November 19.1991 is 13 years and 80 days or 13.22 years. The half life of 137Cs was taken as 30.0 years. Using the standard radioactive decay formula, the fraction of the activity remaining on the calibration date is 0.737. Thus the expected exposure rate is 421 X 0.737 = 310 mR h-1. The pertinent data and results are listed below. ITEM CHAMBER # X1246 CHAMBER #88 Pressure (P) 649 mm Hg 649 mm Hg Temperature (T) 23.3 oC 23.3 oC Scale Reading (SR) 82 units 85 units Normalization Factor 1.176 1.176 Exposure Time (tX) 0.338 h 0.333 h NBS (NIST) Correction Factor 1.06 1.06 Measured Exposure Rate 302 mR h-1 318 mR h-1 Average Measured Exposure Rate 310 mR h-1 Expected Exposure Rate 310 mR h-1 The average measured exposure rate and the expected exposure rate calculated from the calibration certificate supplied with the irradiato r are identical to three significant figures. This high degree of agreement is certainly fortuitous. An agreement to within 5% would be good and agreement to within 10% would be acceptable. Attachments: Victoreen Model 570 R-meter Instruction Manual (copy)

NBS (NIST) Calibration Certificate (copy) Shepherd Irradiator Calibration Certificate (copy)

cc: Bernie Graham, w/o attachments


IDAHO STATE UNIVERSITY TECHNICAL SAFETY OFFICE MEMO DATE: January 6, 1992 TO: Radiation Protection Files FROM: Tom Gesell SUBJECT: Determination of the attenuation factor of the 1.8 cm thick lead attenuator

identified as "1B" used in conjunction with the Shepherd Model 28 "one curie" 137Cs Irradiator, serial number 587.

REFERENCE: Memo to Radiation Protection files from Tom Gesell Dated 12/11/91

entitled: "Check of the primary calibration of Shepherd Model 28 "one curie" 137Cs Irradiator, serial number 587."

This memorandum to file documents a determination of the attenuation factor of the subject attenuator. The measurements were performed in the basement of the Physical Science Building as indicated on the attached data sheets using the same geometry as for instrument calibration. The primary calibration of the subject irradiator was checked previously, see referenced memo. For this determination, the 0.025 R chamber was exposed with and without the attenuator at a distance of one meter. Exposure times were adjusted to give approximately mid-scale readings. The R-meter measurements were made in accordance with the instruction manual attached to the referenced memo. Exposure time, distance and temperature measurements were made with normal commercial devices which were not subjected to any special calibration. Absolute atmospheric pressure was obtained by telephone from the Pocatello NOAA office. The exposure rates (X dot) were calculated in accordance with equations 1 and 2 on the data sheets. From the data sheets the measured exposure rates, rounded to three significant figures, were 316 mR h-1 without the attenuator and 31.7 mR h-1 with the attenuator, yielding an attenuation factor of 0.100. This measured value is reasonably consistent with a simple exponential attenuation calculation using a value of the mass attenuation coefficient of 0.1137 cm2 g-1. Thus use of attenuator "1B" reduces the exposure rate of the irradiator by a factor of 10. cc: Bernie Graham, w/o attachments


IDAHO STATE UNIVERSITY TECHNICAL SAFETY OFFICE MEMO DATE: January 11, 1992 TO: Radiation Protection Files FROM: Tom Gesell SUBJECT: Determination of the attenuation factor of the 3.7 cm thick lead attenuator

identified as "1A" used in conjunction with the Shepherd Model 28 "one curie" 137Cs Irradiator, serial number 587.

REFERENCE: Memo to Radiation Protection files from Tom Gesell Dated 12/11/91 entitled: "Check of the primary calibration of Shepherd Model 28 "one curie" 137Cs Irradiator, serial number 587."

This memorandum to file documents a determination of the attenuation factor of the subject attenuator. The measurements were performed on two separate days in the basement of the Physical Science Building as indicated on the attached data sheets using the same geometry as for instrument calibration. The primary calibration of the subject irradiator was checked previously, see referenced memo. For this determination, the 0.025 R chamber was exposed with and without the attenuator at a distance of one meter. Exposure times were adjusted to give approximately mid-scale readings. The R-meter measurements were made in accordance with the instruction manual attached to the referenced memo. Exposure time, distance and temperature measurements were made with normal commercial devices which were not subjected to any special calibration. Absolute atmospheric pressure was obtained by telephone from the Pocatello NOAA office. The exposure rates (X dot) were calculated in accordance with equations 1 and 2 on the data sheets. From the data sheets the measured exposure rates on 12/17/91, rounded to three significant figures, were 316 mR h-1 without the attenuator and 3.56 mR h-1 with the attenuator, yielding an attenuation factor of 0.0113. Also from the data sheets the measured exposure rates on 1/11/92, rounded to three significant figures, were 320 mR h-1 without the attenuator and 3.69 mR h-1 with the attenuator, yielding an attenuation factor of 0.0115. The average of the two attenuation factor measurements is 0.0114. This measured value is reasonably consistent with a simple exponential attenuation calculation using a value of the mass attenuation coefficient of 0.1137 cm2 g-1. Thus use of attenuator "1A" reduces the exposure rate of the irradiator by the factor 0.0114. cc: Bernie Graham, w/o attachments


Gamma Ray Scintillation Spectrometry Part I: The SCA

OBJECTIVES:

1) The student will calibrate a single channel analyzer. 2) The student will obtain differential and integral spectrums of a Cs-137 source. 3) The student will calculate LC, LD, and MDA values for an unshielded and shielded NaI(Tl) scintillation detector.

INTRODUCTION: Scintillation detectors in combination with solid state detectors are the work horses of nuclear and especially gamma ray spectrometry. The two instruments which are most commonly used for detecting gamma rays are the Na(I)Tl scintillator, and the intrinsic(Ge) germanium detector. NaI(Tl) and germanium both have high attenuation and energy absorption coefficients indicating that they interact well with gamma radiation. Both have good energy resolution meaning that gamma rays with different energies can be resolved. The resolution of the germanium detector, however, is far better than that of the NaI(Tl) detector. However, this advantage of germanium is offset by the fact that its efficiency for the size of detector that most can afford is much less than the efficiency of a relatively inexpensive NaI(Tl) crystal. In addition, at energies above approximately 10 MeV, the efficiency of a germanium detector is essentially zero, leaving scintillators such as NaI(Tl) as the only choice(s). In addition, gemanium detectors must be operated at liquid nitrogen temperature. This requirement leads to considerable expense and inconvenience. Because of these two disadvantages of the germanium detector, the Na(I)Tl crystal continues to be used for all applications except when gamma rays with closely spaced energies must be resolved for identification or quantitative measurement. This and the following laboratories will be devoted to learning about the NaI(Tl) scintillator for gamma spectroscopy. Many of the details of gamma spectroscopy are shared between solid state germanium detectors, considered to be high resolution detectors, and NaI(Tl) detectors which are considered to be relatively low resolution detectors at low energies. All measurement instruments must be calibrated. Even the simple meter stick is calibrated so that the rulings correspond to the primary standard of length, which is now the wavelength of a certain atomic transition in Kr-86. It should not be surprising, therefore, that the scintillation counter must be calibrated prior to use. We often consider three types of calibrations for this type of equipment; energy calibrations, efficiency calibrations, and FWHM calibrations. The first two are used directly in quantitative measurements. The last is useful in analysis of detector operation and in AAAAresolving@@@@ closely spaced peaks. In a scintillation counter, a gamma ray with a given energy will deposit this energy in the NaI(Tl) crystal by both excitation and ionization. Only the amount of excitation is important, and this amount is proportional to the energy of the gamma ray. All interactions


eventually result in excitation, even those which have started as ionization events. Remember, ionized electrons lead to the excitation and potentially ionization of the material through which they pass. Excitations lead to a series of light flashes which will, in turn, cause the emission of a certain number of photoelectrons at the photocathode, the number again being proportional to the energy of the incident gamma ray. For a given probe, which includes the crystal and the photocathode, nothing can be done to alter the number of photoelectrons produced. If the dynode system of the photomultiplier tube is operated at a high voltage, there will be multiplication of the photoelectrons. That is to say that the number of photoelectrons originally produced will speed to the first dynode. When they collide with the first dynode they will deposit their kinetic energy. Most of this was obtained by the potential difference (volts) existing between the photocathode and the first dynode. The energy deposited in this dynode from each electron then cause the emission of more than one (typically 4-5) secondary electrons. These, in turn, experience the potential between the first and second dynode. They accelerate toward the second dynode while gaining considerable kinetic energy. The collision of these electrons with the second dynode results in the production of yet greater numbers of new secondary electrons. There is a gain of 4-5 times more electrons at each dynode, and the total number of electrons after each dynode has been hit can be very large (1E6 - 1E9). This increase in the number of electrons is called multiplication. The magnitude of multiplication depends on the voltage applied between dynodes. After multiplication, via dynodes, the electrons arrive at an anode where a signal pulse is obtained. Although the size of the pulse collected at the anode increases with the voltage applied, there is a practical limit to the size of pulse which can be obtained. When the voltage between dynode stages is too great, one induces spontaneous electron emissions (sparks) from the dynodes. These are multiplied at each stage producing extraneous noise pulses or, worse, permanent damage to the photo-tube. The magnitude of the pulses produced using NaI(Tl) crystals and a photomultiplier tube are typically on the order of several millivolts or larger. It is possible to amplify the pulses produced from a photomultiplier tube with modern amplifiers but commonly a preamplifier is used for improved signal characteristics. The output of an amplifier is usually a positive gaussian shaped pulse with a magnitude between 0 and 10 volts. If the amplifier is linear, which is a requirement for spectroscopy, the sizes of the output pulses will be directly proportional to the sizes of the input pulses. Care should be taken to assure that the amplifier gain is not to great because if the amplifier gain is too large, the amplifier ====s linearity can not be maintained. This situation is called amplifier overload.


Linearity is lost when overload begins. Once a pulse falls within the proper size range, between 0 and 10 volts, it can be counted, or sorted according to size prior to counting. Their size corresponds to the energy of the incident gamma rays which produced them, and thus gamma rays with different energies can be sorted and counted individually. The sorting of the pulse sizes takes place in the analyzer. It is the analyzer that must be calibrated in the scintillation counter. The analyzer has two discriminators, a base (or lower) level discriminator and an upper level discriminator. These discriminators are electronic circuits that produce output pulses (digital) when the (analog) input pulses fall within certain size ranges, the sizes passed depend upon the discriminator settings. A discriminator produces an output pulse when the input pulse is above the discriminator voltage setting. Discriminators are precise potentiometers that operate in the voltage range of 0 to 10 volts. If a (lower-level) discriminator were divided into 1000 increments, (i.e.) if it had a thousand divisions, a setting of 1000 (= 10 Volts) would allow a 10-volt pulse to pass and all smaller pulses would be blocked. A setting of 500 will permit only pulses that are 5 volts or greater to pass. The analyzer may be operated in either of two modes, the integral or the differential. In the integral mode only one discriminator is used (the lower level) and it is used to block and eliminate the large number of small noise pulses which arise mainly from the photocathode. In the differential mode, two discriminators and an anticoincidence circuit are used to establish an energy range in which the pulses must fall to be passed. This energy range is usually called the window and the scintillation counter operating in the differential mode is called a single channel analyzer (SCA). In the calibration of an SCA, it is the base (or lower-level) discriminator that is calibrated. One chooses a gamma ray source that emits gamma rays with a known energy, commonly the Cs-137 (Ba-137m) 0.662 MeV photon is used. The 0.662 MeV photon is a typical energy representative of most commonly encountered gamma rays. One then establishes a window using the base and upper discriminators. This window must be wide enough to allow a narrow range of pulse sizes to get through, but not too wide or the calibration will be inadequate. A window about 20 divisions wide is usually sufficient. The goal is to place the middle of peak in the middle of the window. This can be accomplished by placing the base discriminator at 652 (assuming that the amplifier gain is set so that the 662 keV peak yields a signal with an amplitude of 6.62 volts). With these settings, pulses with a size between 6.52 and 6.72 volts will pass through this window and the SCA will generate an (logical) output pulse. All one has to do to calibrate the system is to place the gamma-ray source in the detector


and adjust the high voltage and amplifier gain (primarily the amplifier fine gain) so the 0.662-MeV gamma ray gives a 6.62-volt pulse. This pulse will slip right through the window and the SCA will generate an output pulse to be counted. The base discriminator, in fact the analyzer, has been calibrated for an energy range of 0 to 1 MeV.

PROCEDURE: 1) Set up the system as described by the laboratory instructor. After the instructor has approved your set-up, turn on the systems power and high voltage. Ramp up the High Voltage slowly to about 1000 Volts. Place a Cs-137 source near the detector. Obtain an oscilloscope trace of each component used. While considering the amplifiers output trace, adjust the focus control potentiometer of the voltage divider. Optimize the output pulse's magnitude using the voltage dividers focus control. Adjust the amplifier to obtain a 6.62 volt pulse. 2. Following the laboratory instructor's directions, obtain both integral and differential spectrums of the Cs-137 source. Plot these spectra as the data is obtained. Also obtain background spectrums in the differential and integral modes. Define in detail each aspect of the differential Cs-137 spectrum. 3. With the detector outside the shield obtain a 5 minute background count. Place the source in the shield and perform another 5 minute background count. Determine LC and LD and MDA for the system over the appropriate Cs-137 region using the backgrounds obtained both inside and outside the shield. Determine the efficiency using the Cs-137 button source in direct contact with the detector for the MDA calculation.


Gamma Ray Scintillation Spectroscopy Part II: The MCA

Objectives:

1) The student will perform an energy calibration of a low resolution MCA spectroscopy system.

2) The student will perform an efficiency calibration of a low resolution MCA spectroscopy system.

3) The student will perform a fit of the FWHM data obtained from a low resolution NaI(Tl) spectroscopy system.

4) The student will plot a Cs-137 (Ba-137m) spectrum and identify each spectral feature and its cause.

5) The student will evaluate the LC, LD, and MDA values of the various components of the NaI(Tl) detector background shields used in the laboratory.

6) The students will experimentally determine the linear absorption coefficient of lead for a Cs-137 source.

DISCUSSION: MCA CALIBRATION The majority of gamma ray analyses performed today are completed using a multichannel analyzer (MCA). The MCA when used in pulse height analysis mode (PHA) will categorize pulses based on their amplitude. This information is used to develop a histogram showing the number of counts on the y-axis versus differential gamma ray energies on the x-axis. To obtain useful quantitative information from an MCA the system must be properly calibrated. There are three different types of calibrations appropriate to MCA systems. The energy calibration assigns photon energy (i.e. spectrum position) to each channel on the system. The efficiency calibration associates counting efficiency to photon energy. The FWHM calibration determines the relationship between FWHM and energy. This is particular useful when peak fitting algorithms are used to define peak area. Energy calibration starts by first setting the amplifier gain in such a way that the full range of the analyzer corresponds to an appropriate range of energies. For example, one usually desires a 0 to 2 MeV full range response. If 511 channels are to be used (that is to say one is


using a conversion gain of 511) the centroid of the 662 keV full energy peak is placed at channel 169. This comes from the idea that a 2000 keV full energy response using 511 channels corresponds to an energy increment per channel of about 3.9 keV. (2000 keV/511 channels = 3.9 keV/channel). It should be observed that the quotient of 662 keV divided by 3.9 keV/channel is equal to 169 channels. A set of data is then obtained which correlates the channel number and the observed peak centroids of various gamma-ray emitter's. There should be a linear relationship between peak centroid energy and channel number. The efficiency data is obtained by determining the net integrated area under each full energy peak. This value provides the measured count rate from a sample. This value is divided by the known disintegration rate of the sample. The ratio of counts per unit time by disintegrations per unit time is the efficiency. Efficiency is determined for each of the various photon energies available. A plot is made of the log of photon efficiency versus the log of photon energy. The function fitting these data is usually a polynomial function when considering a NaI(Tl) detector's response. It is typically an exponential function when considering high purity germanium - high resolution spectroscopy systems. The FWHM data is obtained by considering the FWHM expressed in units of energy for a series of full energy peaks. The FWHM is one parameter expressing the resolution of a system at a particular energy. Normally the FWHM increase with photon energy. These data are often fit using a polynomial function. GAMMA RAY ATTENUATION


Consider a beam of photons passing through a slab of known thickness. This slab will cause a decrease in the photon number. The photons may be said to be attenuated while passing through the slab. It is known that the photon attenuation process can be described by a first order differential equation. The attenuation coefficient is a key parameter of this equation. It is a constant of proportionality allowing one to equate the decrement in the number of photons with the incident photon population's number and the thickness of the slab through which the photons are passing. The value of the linear attenuation coefficient can be obtained experimentally. PROCEDURE 1) Set up the appropriate NIM equipment required for PHA using a NaI(Tl) detector. Obtain oscilloscope traces of each component to verify proper operation. Initialize the MCA system. The system should be operated in the PHA mode with 512 or 1024 channels. 2) Obtain a Cs-137 source. Count the source. Determine the channel number at which the 662 keV peak centroid falls. Adjust the amplifier gain so that the peak centroid falls in an appropriate region. This is an iterative process. Plot the spectrum and identify all the spectral components present. Describe the physics of each component. 3) Taking a series of 60 second individual counts with each source (provided by lab instructor) a few inches above the detector, obtain the spectra of each of the sources provided. Record, in a tabular form, the energy of each peak produced, the peak centroid, the net area under each peak, and the FWHM of each peak. 4) Origin or a spread sheet program could be used to complete the following task (to be performed after the lab session). Perform a least squares fit of the known photon energies and the channel numbers. The photon energy is on the y-axis, channel number is on the x-axis. Determine the coefficients of the variables in this least squares fit - i.e. the slope and intercept. The intercept ideally should be zero, but often it is slightly different from zero. Perform polynomial fits of the efficiency and the FWHM data as described above. Plot each data set showing error bars (estimate he error with FWHM values). Superimpose on these plots the best fitting curves calculated. Provide the actual functions calculated on the plots. Label the plots adequately; name them and label each axis. 5) With the Cs-137 source about 2 or 3 inches above the detector obtain a 60-second spectrum. Observe the region near channel 54 (or whatever the appropriate channel for backscatter may be). You may or may not be able to observe a backscatter peak. Describe what is observed in this region of the peak. Define what a backscatter peak is.


6) Develop a table and plot the data obtained under the following circumstances. Determine the net counts in the region of interest (ROI) of the Cs-137 full energy peak. Remove the source and obtain a 2-minute spectrum. Remove the outer layer of shield and repeat this procedure. Remove the middle layer of shield and repeat this process. Remove the last layer of shield and repeat this process. Comment about the MDA, LC, and LD under each shield circumstance. Comment on any observations involving a potential backscatter peak. 7) Set up the experimental apparatus to be used for the attenuation experiment as instructed. Using a Cs-137 source obtain a series of 60 second counts. After each count add an additional layer of lead between the source and the detector. Plot the number of counts on the y-axis versus the increasing thickness of lead on the x-axis using a semi-log plot. Determine and report the linear attenuation coefficient of lead which you observed during this procedure.


GAMMA RAY SPECTROSCOPY PART III: High resolution gamma spectroscopy, the High Purity Germanium Crystal

OBJECTIVES:

1) The student will perform an energy and efficiency calibration of the HP(Ge) system.

2) The student will determine the relative efficiency of the HP(Ge) system based on the methods outlined in ANSI/IEEE no. 325 1986.

3) Students will identify all spectral features associated with a Co-60 spectrum.

4) The student will identify the radionuclide in an unknown sample and give its activity (quoted with appropriate error bars).

DISCUSSION: High resolution spectroscopy systems are perhaps the most useful laboratory equipment for the analysis of samples containing unknown radionuclides. They are easy to use, reliable, and dependable. They are also very expensive. A new system may cost anywhere from $20,000 to $75,000. All measurement systems must be calibrated. Students will use a mixed gamma source to perform energy and efficiency calibrations of the HP(Ge) system used in the laboratory. The calibration data sheets provided in class will give all the pertinent information concerning the calibration source to be used. Do not forget to correct for decay of this source. The procedure for performing these calibrations has been given in previous laboratory write-ups. Be sure and plot all curves along with the data generated. An unknown sample will be provided for analysis. Students are expected to correctly identify this source and estimate the activity of this source. Answers are to be expressed in µCi. Students can use any analysis procedure they choose. This must be fully explained in their write up. Along with this explanation should be reasons why each step was taken, and what each bit of information will provide. Students additionally will determine the relative efficiency of the HP(Ge) detector. This is done as follows:

1) Place the provided Co-60 source exactly 25 centimeters away from the face of the


detector. Count the Co-60 source provided by the instructor for 600 seconds. 2) Calculate the absolute full energy peak efficiency by dividing the number of counts (area) in the full energy peak by the number of 1.332 keV gamma rays emitted during that count time. The source information will be provided in class.

3) Calculate the relative efficiency by dividing the absolute full energy peak efficiency by 1.2x10-3 (the absolute efficiency of a 3x3 NaI(Tl) crystal 25-cm from the source.

4) Compare your calculated relative efficiency with that listed on the detector.


Alpha Spectroscopy Surface barrier detectors

OBJECTIVES:

1) The student will perform an energy and efficiency calibration of a surface barrier detector.

2) The student will determine the efficiency of a surface barrier detector system based on the solid angle subtended by the detector.

3) Students will examine the effects of collimation on the resolution of an alpha spectrometer.

4) Students will examine the effect of thin layer foils imposed between the source and detector.

5) Students will identify an unknown alpha source supplied by the instructor.

DISCUSSION: High Resolution alpha spectrometry may be an extremely useful tool for the identification of Transuranics. Alpha spectrometry is relatively simple. It is important to have a good vacuum, a detector with good resolution, and collimation of the source. Charged particles constantly loose energy when penetrating matter. Even the interaction of matter in gaseous can significantly decrease the energy of a charged particles. The rate of energy loss of a charged particle can be determined using the Bethe-Bloch equation. The loss of a charged particles energy between the source and detector results in two things. A shift in the perceived particle energy to the left (i.e. a loss of energy) and an broadening of the charge particle energies measured. The loss of energy expected to be experienced as the particles travel through gas can be reduced by placing the source and detector within a vacuum. Reducing the available gas for interaction reduces the number of potential interactions. The desired magnitude of vacuum for higher resolution alpha spectroscopy should be around 10 microns of vacuum.

Detector resolution is another key aspect of alpha spectroscopy resolution. A reduction in the thickness of the dead or depletion layer on the surface of the detector should increase the detectors resolution. This however, increases the detectors susceptibility to physical damage. Source collimation enhances resolution by decreasing the energy loss in the detector's dead


region. Alpha particles incident on the detectors surfaces at angles much different than the perpendicular will loose increasing amounts of energy as they penetrate increasing thicknesses of dead-layer. Collimator the alpha particles allow only those particle incident at right angles to the detector to interact with the detector thus improving resolution. The simple act of alpha spectroscopy is only a small piece of the alpha spectrometry puzzle. The real art of alpha spectrometry is associated with sample preparation. Typically, samples of alpha emitting radionuclides are electroplated on to the surface of metallic disk in almost a monatomic layer. This reduces the self-absorption of the disk. The necessary preparation steps prior to electro deposition may at times involve complex radiochemical processes. Students will not be asked to prepare such samples during this laboratory session. PROCEDURE:

1) Perform an energy and efficiency calibration of a surface barrier detector/MCA. Additionally, determine the efficiency of a surface barrier detector system based on the solid angle subtended by the detector. The efficiency is determined by evaluating the size of the detector, the distance between the source and detector, and the size of the collimated source.

2) Examine and report on the effects of collimation on the resolution of an alpha spectrometer. Experiment with different columinator-source-detector distances, and multiple collimators. Under which circumstances is the best resolution observed.

3) Determine the LC and LD of this counting system for alpha particles.

4) Examine the effect of thin layer foils imposed between the source and detector. Does this correspond to what was expected based on the Bethe-Bloch expression?

5) Students will identify an unknown alpha source supplied by the instructor.

Liquid Scintillation Counting

OBJECTIVES: After completion of this lab, the student will be able to:

1. Calibrate the liquid scintillation counter for t ritium measurement. 2. Differentiate background counts resulting from samples prepared from distilled and undistilled water. 3. Determine the gross-alpha activity of radionuclides collected with a swipe. 4. Determine the effect of pH on the scintillation cocktail.


DISCUSSION:

Liquid scintillation detectors depend upon the emission of light which results from the interaction of radiation with a liquid fluorescent material. When radiation interacts with a molecular fluorescent material, molecular electrons are raised to an excited energy state. When these electrons return to their ground state, light photons are emitted. If these photons interact with a photomultiplier tube (PMT), these flashes of light are converted to an electrical pulse which can be measured with supporting electronics.

Organic scintillating materials used for liquid scintillation counting consist of relatively large organic molecules. These molecular compounds generally have conjugated double bonds. Excitation results from radiation interaction with the pi electrons on the organic molecule. The decay times associated with this excitation is very short. Typically between 1 x 10-8 to 1 x 10-9 seconds.

Typically, liquid scintillation solutions are comprised of a scintillating organic solute and solvent. The solvents which were used during the earlier years of liquid scintillation counting are now often classified as hazardous organic materials (e.g. Toluene and Xylene). Due to the hazardous nature of the solvent and the possibility of relatively high concentrations of radioactive materials in the solution, scintillation samples could be considered as being mixed waste. Recently, nonhazardous organic solvents have become more commonly used.

To accomplish liquid scintillation counting, the walls of the vial containing the cocktail must be transparent to light. Because of this, it is imperative to avoid labeling the side of the vial or getting fingerprints on the side of the vial. Reduction of scintillation efficiency or the absorption of photons by materials present on the inside or outside of the vial before the photons reach the photocathode is referred to as quenching.

Typically, the scintillating medium (cocktail) contains an organic solvent and one or more solutes with other materials sometimes added to enhance performance. The sample being measured is either dissolved or suspended in the scintillation solution. The vial containing the cocktail and sample is then placed between two PMTs during the counting process which are operated in coincidence to reduce noise.

Since the number of solvent molecules is significantly larger than the number of solute molecules, radiation is likely to interact with the solvent before it will interact


with the solute. The energy of the excited solvent molecule is then transferred to a solute molecule. This occurs rather rapidly. The excitation energy received by the solute molecule is eventually converted to a light photon which may interact with the PMT and be measured/detected by the supporting electronics.

PROCEDURE Tritium Calibration (Specification Verification)

Many liquid scintillation counting systems can be calibrated automatically to ensure that the system is operating properly. This is accomplished by setting the energy-pulse height response curve. The counting system used in this laboratory will be explained by the laboratory instructor. Each laboratory group will prepare a series of samples. Some of the samples will be prepared in order to develop quench correction (efficiency) curves as explained in class. Other samples will be prepared as unknowns for analysis.

Calculate percent efficiency as follows:

%Efficiency = [cpm - background] X 100%

dpm (with half-life correction) Background Sample Preparation

1. Obtain two 20-mL scintillation vials from the instructor. Fill the sample vials with 10 mL of scintillation cocktail. Fill one sample with 10 mL of distilled water and the other vial with 10 mL of undistilled (tap) water. Place the lids on the sample vial and tighten them securely. Mark the lids of the sample vials to differentiate the distilled water sample vial from the undistilled water sample vial.

2. Place the samples in the detector, as instructed. Dark adapt the counter and count the sample for 30 minutes. Record the results in your notebook.

Swipe Test

1. Prepare a liquid scintillation vial and cocktail as instructed. Using a filter paper, collect dust which has accumulated on a 100 cm2 area on a computer screen. Place the filter paper in the scintillation vial so that the side which collected the dust is facing towards the center of the vial. Place lid on the vial an tighten securely. Repeat the process on a different 100 cm2 area on the same computer screen for a second filter paper. But this time, place the filter


paper in the scintillation vial so the side which collected the dust is facing away from the center of the vial.

2. Place both sample vials in the liquid scintillation counter and perform a gross alpha count for 30 minutes. Record results in your notebook.

Quench Correction

1. Prepare five liquid scintillation vials for counting (i.e. fill with cocktail as prescribed by lab instructor). Place increasing amounts of nitromethane varying from 0 to 90µL in each of the five samples. Add a known constant amount of tritiated water to each of the five samples. These samples will each be analyzed with the specific purpose of developing an efficiency versus quench indicating parameter (QIP) curve.

2. The laboratory instructor will provide an unknown spiked sample to you for analysis. Using the efficiency versus QIP


NEUTRON DETECTION LAB OBJECTIVES:

1) The student will be able to describe the operational theory of the BF3, proportional detectors and scintillation detectors used to detect and measure neutrons.

2) Students will gain experience measuring and describing neutron energy spectra associated with various types of neutron energies and various detectors.

INTRODUCTION: Neutrons are indirectly ionizing particles. The probability of neutron interaction is a function of their energy and the interactions properties of the materials with which they interact. The detection of neutrons depends on their ability to interact with a detection material. Neutron detectors measure reaction products (in the case of nuclear reactions) or secondary ionization (in the case of low-Z proton-recoil scintillators).

1) Set up the BF3 ion chamber system described during lecture.

2) With a provided neutron source, experimentally develop a curve of observed counts versus applied voltage in order to determine the saturation voltage of the BF3 ion chamber system. Measure the detector spectra versus various moderator thicknesses and describe and explain the spectral features. Estimate the detector efficiency versus moderator thickness. Could you use a BF3 detector as a dosimeter?

3) Repeat the above with a plastic scintillator.


TLD Lab OBJECTIVES:

1) Students will become familiar with the theory of thermoluminescent dosimeters. 2) Students will calibrate a batch of TLD chips and then use their calibration to determine the exposure received by a second group of chips.

DISCUSSION: Thermoluminescent dosimeters (TLDs) are based on the property of thermoluminescence, which can be understood if one refers to the electronic energy-band diagram of crystals. When ionizing radiation bombards a crystal, the energy given to the electrons may bring about several results. The electron may acquire enough energy to move from the valance band to conduction band, in which case the event is called ionization. An exciton, consisting of an electron and a hole bound electrostatically, can migrate through the crystal. Electron, holes, and excitons may be caught in many traps that exists in the solid. Traps are formed in a variety of ways. Impurities, interstitial atoms, dislocations, vacancies, and imperfections may act as traps. The trapped carriers remain in place for long periods of time if the temperature of the crystal remain constant or decreases. If the temperature is raised however the probability of escape increases. To obtain information about the amount of energy deposited within the dosimeter, the TLD is heated under controlled conditions. As the TLD is heated it emits light. Light intensity is measured either as a function of temperature or a function of the time during which the heat is being applied to the crystal. The result of such a measurement is a special plot called a glow curve. The peaks of a glow curve correspond to the energy levels of various energy traps in the crystal. Each level of energy trap has its own binding energy. The amplitudes of the peaks are proportional to the number of carriers trapped in the corresponding energy traps, which in turn is proportional to amount of energy absorbed from the radiation. The intensity of the light emitted from the thermoluminescent crystals is thus directly proportional to the radiation dose. In order to enhance the probability of visible photon emission during the de-excitation process, small amount of impurity are sometimes added to the crystal. These impurities are called activators. They create special sites in the lattice in which the normal energy band structure is modified from that of the pure crystal. As a result, there will be energy states created within the forbidden gap through which the electron can de-excite back to the balance band.

Operation


The sample is commonly processed in a TLD reading instruments called a TLD reader, which automatically heats the material, measures the light yield as a function of temperature, and records the information in the form of a glow curve. A basic TLD reader consists of a well controlled heat source, a photocathode and a photomultiplier tube, and an output recording device. After exposure, the TLD material is heated, as the temperature rises trapped electrons and holes migrate and combine. This is accompanied by the emission of light photons. Some of the photons enter a photomultiplier tube and produce an electronic signal. This may be displayed using an X-Y plotter to develop a glow curve. More frequently, the total light output is integrated electronically and displayed in digital form. The total light output or the area under the glow curve (the integrated light output) can be compared with the output from calibrated TLDs to infer radiation dose. There are many thermoluminescence materials, but the ones which are useful for dosimetry should have the following characteristics.

1. Retention of trapped charge carriers for long periods of time at temperatures encountered during the exposure 2. Large amount of output 3. Linear response over a large dose range 4. Perfect annealing to enable repetitive use

Materials that satisfy most of these requirements are CaSO4 : Mn, CaF2 (natural), CaF2 :Mn, Li 2B4O7:Mn and LiF. From the above materials LiF has been used most widely because of their large dose range, good material stability and approximate tissue equivalence properties. LiF has a linear dose response up to around 1X105 rad, and the sensitivity of about 10 mrad. The TLD-100 containing natural lithium (92.6% 7Li, 7.4% 6Li) responds to gamma and thermal neutrons. Thermal neutrons are detected through the (n,alpha ) reaction with 6Li, which has a cross section equal to 950 b for thermal energies. The TLD-600 containing lithium enriched to 95.62 percent in 6Li, is extremely sensitive to thermal neutrons and also to gamma. The TLD-700 containing 99.993 percent 7Li, is sensitive to gamma only, because the neutron cross section for 7Li is very small (about 0.033 b for thermal neutrons). Calibration and annealing techniques The TLD reading instrument is calibrated by measuring the intensity of light from phosphors that had been exposed to known doses of radiation. Since the intensity of luminescence is proportional to the quantity of phosphor as well as to the absorbed dose, the amount of


phosphor used in making a measurement must be kept as close as possible to the amount used in calibrating the instrument. When the TLD is annealed, it returns to its original condition; it is ready to be used again. During the annealing process the TLD is heated long enough so that all the traps within the crystal can be emptied. The sensitivity of the dosimeter strongly depends upon the annealing technique and the dosimeters thermal history. Different annealing techniques are used for different types of chips. LiF phosphor generally requires a one hour annealing at 400EEEEC to reset the phosphor to its original condition. Following this annealing, the dosimeters should be rapidly cooled to nearly room temperature a process which should take about 2 minutes. The chips are then heat treated overnight (24 hours) at a temperature of 80EEEEC. The accurate measurement of low exposures( less than about 400 mR) requires the use of gas flow (usually dry N2 gas is used) to blanket the dosimeter. This reduces spurious luminescence. Gas flow is also used for the measurements of extremely high doses. This has the added advantage of retarding the formation of tarnish on the stainless steel heating pan. PROCEDURE

1. Six batches of TLD chips will be irradiated using the Cs-137 Shepard irradiator to various levels of absorbed dose. Each batch will contain 5 TLD chips. The 6 levels of absorbed dose used will span the range from 10 mRad to 1000 mRad. Students will readout and record the light output produced from this batch of chips. The data collected from these chips will be used to develop a calibration curve which will in turn be used to identify the unknown dose delivered to 3 other sets of dosimeters.

2. To use the TLD reader follow the instructions given in class.

3. After reading all of the dosimeters in the "calibration group" read the three sets of dosimeters exposed to an "unknown dose". Report these values in your laboratory write up.


STUDY GUIDE

1. What does an oscilloscope measure? 2. List and identify the function of the eight primary components of an oscilloscope. 3. How is the oscilloscope's trigger system activated? 4. Distinguish between normal and automatic trigger modes. 5. Sketch the shape of a typical pulse as that shown on an oscilloscope display. Identify

and define the characteristic values used to describe the shape of the pulse. 6. A pulse has an amplitude of 2.4 divisions. Determine the magnitude of the pulse is

the vertical deflection is set at 0.5 volts per division. 7. 4.5 divisions separate the crests of a typical sinusoidal wave pulse. Determine the

frequency of the wave if the sec/div control is set at 2 ms/div. 8. What is the function of a NIM bin? 9. List advantages of using NIM standard equipment. 10. List disadvantages of using NIM standard equipment. 11. What is the purpose/function of a pre-amplifier? 12. Sketch the output pulse produced by a pre-amplifier. 13. What is the purpose/function of an amplifier? 14. Sketch the output pulse produced by an amplifier. 15. What is the purpose/function of a Single Channel Analyzer? 14. Sketch the output pulse produced by a Single Channel Analyzer. 15. What is a discriminator? 16. List and differentiate the discriminator modes which can be used by a Single Channel

Analyzer. 17. What is the purpose of a high-voltage supply? 18. What are the functions of scalers, timers, counters? 19. Sketch the count rate vs. voltage curve for gas-filled detectors and identify the various

regions. 20. Define/differentiate the various regions of the six-region curve. 21. What is dead time? 22. What is resolving and recovery time? 23. How can dead time be determined for a GM detector? 24. Sketch the output pulse produced by a GM detector. Determine tr, td, and voltage of

output pulse. 25. Define and explain the concept of radioactive decay. 26. List possible sources in which to find the radioactive half-lives for various radionuclides. 27. What is the relationship between the decay constant and half-life for a particular

radionuclide?


28. Define average (or mean) life. 29. What is backscattering? 30. What factors influence backscatter? 31. How can the identity of an unknown radionuclide be determined? 32. Define accuracy. 33. Define precision. 34. Define error. 35. Identify and define the different sources/types of error. 36. List and differentiate the three types of statistical distributions. 37. What type of distribution best describes radioactive decay? Explain. 38. For each of different statistical distributions, how are the variance, standard deviation,

and relative error determined? 39. Describe the method used to determine whether or not a collection of data is random

or if systematic trends exist in the data set. 40. Determine the propagation of error expression for the following algebraic expressions.

a. R = [(Counts) - (Background)] [(efficiency)(air volume sampled)(count time)]

if air volume = (flow rate) x (sample time).

b. x = 1/[2(u + v)] c. x = uv2 d. x = u2 + v2

41. Sketch the output pulse produced by a gas-filled proportional counter. Determine tr, td, and voltage of output pulse.

42. What is gas multiplication? 43. What accelerates the ions produced within the gas volume of a gas-filled

proportional counter after an ionization event? 44. What region of a cylindrical gas-proportional counter does ionization occur? 45. What type of radiation does a gas-proportional counter detect? 46. Why is the pulse produced by an incident alpha particle larger than the pulse produced

by an incident beta particle? 47. What determines the efficiency of a gas-filled proportional counter? 48. What is the purpose of fill-gas? 49. What is quenching? 50. A ten minute count of a radioactive sample produces 100,190 counts. Determine

LD, LC, and MDA values for this detection set up if a ten minute background count results in 10,000 counts.

51. With regard to environmental monitoring, what methods are used to obtain air


samples? 52. Differentiate the different methods of determining radionuclide concentrations in air. 53. What is the KOVAL method? 54. Describe how the KOVAL method can be used to analyze environmental samples. 55. What is detector efficiency? 56. How is detector efficiency determined? 57. What factors influence a detector's efficiency? 58. What is the inverse-square law? 59. How is the inverse-square law used to calibrate a radiation survey meter? 60. What is attenuation? 61. How is attenuation used to calibrate a radiation survey meter? 62. What units are displayed on a radiation survey meter? 63. What does a radiation survey meter measure? Explain. 64. What is ALARA? How should ALARA be applied with respect to laboratory experiments performed in this laboratory course?

2012-labman

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