Source Calibration for Neutron Flux Measurement

K.Craycraft

19 July 2012

Abstract

The NPDGamma experiment is currently running at the Fundamental Neutron Physics Beamline(FNPB) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL). The goalof the experiment is to measure the parity-violating asymmetry between the incident neutron spin andemitted photon direction for the capture of neutrons on protons. The gamma-rays are detected in aCsI array. We need to know the neutron ux accurately to verify that we are running at countingstatistics. We measure the neutron ux from the gamma signal produced by capturing all neutrons ona black boron target. The detectors were calibrated with a known gamma-ray source (Cesium-137) tohigh precision using a High Purity Germanium (HPGe) detector. This paper presents methodology andresults of calibrating a cesium source for use in calibrating cesium iodide detectors for measurements ofneutron ux.

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Contents

1 Introduction to Facilities 31.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Spallation Neutron Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.2 Fundamental Neutron Physics Beamline . . . . . . . . . . . . . . . . . . . . . . . 3

2 NPDGamma Experiment 42.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Data Acquisition System (DAQ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Neutron Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Methods 7

4 Materials 84.1 High Purity Germanium (HPGe) Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Weak Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Strong Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Mass Attenuation Coecient (MAC) Corrections 95.1 Pressure in calculation of air density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.2 Weak Source Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.3 Strong Source Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6 Analysis and Results 116.1 Weak Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.2 Strong Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7 Discussion 12

8 Acknowledgement 12

References 13

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1 Introduction to Facilities

1.1 Overview

1.1.1 Spallation Neutron Source

Figure 1: SNS Campus

The SNS (gure 1) at Oak Ridge National Laboratory consists of several dierent buildings that worktogether to produce spallation neutrons.

An ion source within the Front-End Systems creates negatively charged Hydrogen atoms (one proton andtwo electrons) that are accelerated through three types of linear accelerators (a radio-frequency quadrupole,a drift-tube linac, and a coupled-cavity linac) to an energy of 185 MeV. In order to achieve an energy of 1 GeVthe beam is then accelerated by a succession of superconducting radio-frequency cavities. The acceleratedions are stripped of their electrons by a foil stripper to create a proton beam. This proton beam enters theaccumulator ring where it is intensied by completing 1060 loops around the ring. The accumulator ringreleases a pulse of protons 70nS in size to the target at a rate of 60 Hz.

Figure 2: Target Diagram

In gure 2 the proton beam moves from right to left to strike the liquid Mercury spallation target. Atfull power the proton beam is 1-GeV in energy, 1.4 MW directed on the target with a beam current of 1.4mA[1]. On average 20-30 neutrons are ejected from each Mercury atom and depending on which direction theneutrons are spallated the neutrons are moderated by supercritical liquid hydrogen (for cold neutrons) orwater (for thermal neutrons). These neutrons are guided down beam lines and into instruments.

1.1.2 Fundamental Neutron Physics Beamline

Beamline 13 at the SNS is an intense cold neutron beamline dedicated to measuring and examining theneutron through experiments such as neutron lifetime, neutron decay correlations, neutron electric dipole

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moment, as well as measuring the interaction of the neutron with targets such as Hydrogen, Chlorine, Boron,and Aluminum[2].

Figure 3: Fundamental Neutron Physics Beamline Diagram

In gure 3 the beam follows a beam guide from the top left moving towards the bottom right. In thedirection of the target there exists a beamguide as well as a primary shutter which is used in order to stop thebeam entrance into the experiment. This primary shutter is a thick slab of concrete and Tungsten and is onlyused when the accelerator is down for long periods of time. There currently exists 2 rotating mechanicaldevices known as choppers which are able to prevent neutrons from dierent pulses from entering thedetector array at the same time.

This beamline has the capability of running two experiments simultaneously through the use of amonochromomater. A monochromomater is a device that can select certain wavelengths of radiation froma larger range of wavelengths. The monochoromater installed at FNPB selects 8.9Å neutrons to pass downbeamline 13A (the Ultra Cold Neutron beamline) while those neutrons that are passed by the choppers andthe monochoromater continue down beamline 13B (Cold Neutron beamline) [3].

2 NPDGamma Experiment

2.1 Overview

Figure 4: NPDGamma reaction

NPDGamma strives to measure correlation between the neutron spin and the photon direction by direct-ing a neutron beam into a target of liquid hydrogen in order to better understand the weak force interactionbetween nucleons.

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When a neutron captures on the nucleus of an atom, the resulting nucleus is in an unstable, excited state.In order to return to the ground state, the nucleus can lose its excess energy by emitting radiation in theform of an ionizing particle. In the case of the NPDGamma experiment, this ionizing particle is a gammaray. There is a correlation is manifest as an asymmetry between the spin of the incoming neutron and theresulting gamma ray that is created from neutron capture. It is this asymmetry that NPDGamma strives tomeasure to a 10−8 uncertainty.

Figure 5: Diagram of NPDGamma Experiment

In gure 5 The unpolarized neutron beam enters from the left side of the diagram and travels towardsthe right, encountering a number of devices that prepare it for entrance into the experiment cave. A shutterof Tungsten and steel acts as a control mechanism to allow or stop the beam from entering the cave.

Neutrons are characterized by their time of ight (TOF), which is found by knowing the position of apulse at two dierent locations and the time that it takes that pulse to travel the distance between those twopoints. This allows for the velocity, energy and wavelength of the neutron to be found. The NPDGammaexperiment only nds useful neutrons between 2.5 and 6 Å and in order to select this band of neutrons achopper is used. A curved 17 m neutron guide made of glass with a supermirror coating of Nickel andTitanium extends from the moderator [4] to beam monitor 1 (m1) and leads the beam through two choppers.Because the neutron pulse consists of neutrons traveling at dierent velocities (which means dierent energiesand dierent wavelengths) the chopper has a small aperture which revolves at a high rate. This rotatingwindow is open to the beam for small periods of time in which only neutrons with the proper speed will beemitted through. Thus, neutrons that are too fast or too slow are likely to be rejected from one chopper orthe other.

Supermirror polarizer constructed of Iron (a reector) and Silicon (a transmitter) which acts as a lterin order to reect a one spin state, but transmits the other spin state through the supermirror coating andinto the boron glass. Boron has a high capture cross section and thus absorbs these neutrons to emit 0.5MeV gamma rays that are shielded from the detector with plates of lead. The polarized beam enters the spinipper (SF) which eciently ips the neutron spin up or down by creating an oscillating magnetic eld tunedto the Lamour frequency of neutrons [5]. The polarized beam captures on the target, resulting in neutroncapture on cold hydrogen which creates 2.2 MeV Gamma rays that are detected with CsI crystals. The entireexperiment is placed in a 10G eld to maintain the polarization of neutrons that exit the polarizer.

2.2 Data Acquisition System (DAQ)

The accelerator operates at 60 Hz (or that is to say that the accelerator releases a pulse of protons to thetarget every 16.67ms), and once an accelerator pulse arrives at the SF the neutrons of each pulse can remainspin up (+1) or rotated to spin down (-1). The SF ips the neutron spin of a series of pulses into a patternknown as a spin sequence of -1;1;1;-1;1;-1;-1;1. By performing this pattern it is possible to eliminatesystematic errors. This spin sequence constitutes 8 accelerator pulses. The ninth accelerator pulse is notrecorded as it is the time in which data is read from the previous spin sequence[6].

There are eight accelerator pulses in a data pulse, and a data pulse is made up of 320 time bins with atime bin interval of 0.4 ms.

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2.3 Neutron Flux

NPDGamma's goal is to measure asymmetry to the statistical uncertainty given by equation 1

δAH ≈1√N

= 10−8 (1)

and by using the equation of goal counts

N = T · F · fcap · (Ω/4π)⟨cos2 θ

⟩· rps · fframe · fread · P 2 (2)

where T is the time to reach goal number of counts, F of the neutron beam given in neutrons/sec, fcapis thefraction of neutrons that capture on liquid H2 (a well known number),(Ω/4π)/

⟨cos2 θ

⟩is the consideration

of geometrical factors (consequence of the detector setup), rps is the error uncertainty, fframe is the fractionsof neutron in a frame (consequence of the choppers), fread is the time lost to read out data (consequenceof the data acquisition system), and Pol is the polarization of the neutron beam (consequence of the superpolarizer)[7].

In order to calculate the neutron ux [8], two dierent voltages need to be measured by the detectorarray. One voltage source is a strong Cs-137 source placed directly in the center of the array with the shutterclosed (Fig. 7), and the other source is a boron plate placed at a 45º angle with the shutter open to allowfor the neutron beam to strike it (Fig. 6).

Figure 6: Boron plate placementFigure 7: Cesium source placement

The voltage per time bin measured by the detectors for the Cs source is given by

vCs = BCs ·MCs ·Gi · Sm (3)

where BCs is the branching ratio of Cs-137,MCs = ΩCs,iEγ,Cs is the detector energy deposition (this numberis given by the neutron simulation software MCNPX), Gi is the detector gain, and Sm is the Cs-137 sourcestrength in disintegrations per time bin.

The voltage per time bin measured by the detectors for the Boron plate is given by

vB = MB ·Gi ·4Nλ4tb

(4)

where MB = BBΩB,iEγ,B is the detector energy deposition multiplied by BB , the fraction of gammas thatare emitted from excited barium transitioning to the ground state (this number is given by the neutronsimulation software MCNPX), Gi is the detector gain, and

4Nλ4tb are the number of neutrons per time bin.

By rewriting 3 and 4 the number of neutrons per time bin 4Nλ4tb can be found, and when multiplied by60 Hz (the rate at which accelerator pulses are directed into the target), a formula for ux per time bin canbe found

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∆Nλ∆tb

= 60 · vBvCs·BCs ·

(MCs

MB

)· Sm (5)

This calculation of neutron ux was performed 2 July 2011. The strength of the source, Sm, that was usedto calibrate the detectors must be known to 1% accuracy in order to avoid any systematic errors. The goalof this paper is to outline the post-calibration of this gamma ray source.

3 Methods

Two sources were used in this experiment. The rst was the 5.2 mCi source used on 2 July 2011 in orderto calculate the neutron ux. This is the source whose strength needs to be found within 1%. The secondsource is a calibrated 40.89 µCi source (referred to as the weak source).

A radioactive source can be treated as a point source where gamma rays are emitted in a 4π solid angle.Only one detector was used therefore only a fraction of these emitted gamma rays are accepted by thegermanium detector. Thus, the when calculating the rate emitted by the source, it is necessary to take thesolid angle into consideration in the formula.

Inside the detector capsule there is a germanium crystal that is set a distance r0 from the detector face.A rate Rµ is detected by the germanium crystal but the distance measured is from the detector face to thesource. This means that the true distance that corresponds to a Rµ is (d-r0).

Figure 8: Diagram of experiment

Thus for dead time << 1 and detector-source distance, d >>√A the equation

Rµ =SµA

4π(d− r0)2(6)

describes the Rµ in [neutrons/s] detected at the germanium crystal where Sµ is the strength of the calibratedweak source, A is the area of the detector face, d is the distance from the detector face to the source, and r0is the distance from the detector face to the germanium crystal.

The weak source was placed at diering distances of 20 cm to 100 cm in 20 cm increments, 100 cm to 500cm in 100 cm intervals, and 6 measurements where the source was placed at 500-510 cm. Each measurement(called a run) was taken long enough in order to accumulate at least 10000 counts underneath the Cs-137662 keV photopeak. After a room background was subtracted from each of the runs, the background of thephotopeaks were t with a rst degree polynomial in order to subtract the detector background.

Rewriting equation 6 it can be seen that by plotting 1√Rµ

versus d and performing a least squares t

a slope and an intercept can be found. In gure 9 there is a positive slope, positive y-intercept, and anegative x-intercept which corresponds to the distance in which the germanium crystal is located inside of

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Figure 9: A sketch of expected results

the detector capsule.

Rewriting equation 6 for use with the strong source placed at a xed distance away from the detector

(d− r0)2 ·Rm =SmA

4π= C (7)

equation 7 shows that the number of gammas per second emitted by the strong source multiplied by thedistance between the front of the germanium detector and the source squared is equal to a constant. Thissame constant is equal to the source strength of the gamma ray source multiplied by the are of the detectorface divided by 4π . By taking multiple measurements at this distance and taking the weighted average thevalue of C can be found.

By using equations 6 and 7 it is possible to nd the ratio of Sµ and Sm as described by the equation

SmSµ

= C ·m2µ (8)

and by using the Sµto be 34.98 µ Ci it is possible to calculate the strong source strength Sm.

4 Materials

4.1 High Purity Germanium (HPGe) Detector

The detector used for this experiment is an ORTEC GMX Series GAMMA-X HPGe coaxial photon detectorwith a crystal diameter of 51.6 mm and crystal length of 54.5 mm. It has a relative eciency of 20%. Thisdetector operated with a NIM bin with two cards. The detector operated at -3500 Volts DC (as dialed onthe ORTEC 660 Dual 5k Bias supply), with an overall gain of 25 and a pulse shaping time of 3µseconds (asdialed on the ORTEC 672 Spectroscopy Amplier).

4.2 Weak Source

The weak source used is a Cs-137 source dissolved in 5ml of water and contained in a ame sealed NISTborosilicate-glass (pyrex) ampoule. This source has an uncertainty provided by NIST of 0.7%.

On 30 September 2005 the strength of the source is 40.89 µCi. Using the half life of Caesium and thetime between the calibration date and analysis date being 2474 days, the calculated theoretical strength ofthe weak source was 34.98 µCi.

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Figure 10: HPGe Detector Figure 11: NIM Bin

Figure 12: Front view of calibrated source Figure 13: Back view of calibrated source

4.3 Strong Source

The strong source is a Cs-137 ceramic pellet of 3.0 mm diameter doubly encapsulated with 3.0 mm of stainlesssteel. The analysis date of 20 July 2012 (3811 days since calibration) gives the strong source a calculatedtheoretical strength of 4.09 mCi.

Figure 14: Strong source schematic Figure 15: Side view of strong source

5 Mass Attenuation Coecient (MAC) Corrections

Materials exist between the germanium detector crystal and the gamma ray source that cause gamma raysemitted from the source to be scattered or absorbed as they travels toward the detector. This causes the rate

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detected by the detector to be less than actually emitted from the source. The strength of this scattering isgiven by the a mass attenuation coecient (MAC), that depends on the energy of the gamma ray emittedby the source as well as the type and density of the material between the source and the detector.

Figure 16: Diagram of experiment with MAC considerations

The equation

I = I0e−(µ/ρ)·ρd (9)

describes the relationship between the corrected intensity I, the original intensity I0, mass attenuation coef-cient (µ/ρ) in cm2/g, and d is the distance in meters. The µ is called the linear attenuation coecientand when it is divided by the density, ρ, it becomes the mass attenuation coecient. The linear attenu-ation coecient is dependent on density, therefore using the mass attenuation coecient instead producesa constant for a particular compound or element. There exists a NIST database Tables of X-Ray MassAttenuation Coecients and Mass Energy-Absorption Coecients [9], but the intervals of reported MACwere large and to use them would prove to be inaccurate. A dierent NIST database XCOM: Photon CrossSections Database [10]was used to precisely calculate the total attenuation coecient, and for compounds(Polyethylene, Pyrex, Air) the NIST composition database Stopping-Power and Range Tables for Electrons,Protons, and Helium Ions was used for calculating density and chemical composition for use with the PhotonCross Sections Database [11].

Using 9 and information provided by NIST the corrected photon rates were found.

5.1 Pressure in calculation of air density

Information on Mass Attenuation Coecients for dry Air were given at an elevation of sea level. The airdensity higher elevations is lower than the air density at sea level and corrections were necessary. Using theequation for air pressure

p = 101325 · [(1− 2.25577× 10−5) · h]5.25588 (10)

where p is in Pascals and h is in meters. Oak Ridge, Tennessee is located 259 m above sea level, thus theair pressure is 98250 pascal. This air pressure is inserted into

ρ =p

Rspe · T(11)

where ρ is in grams/cm3, p is air pressure in Pascals, Rspe is the specic gas constant for dry air (287.058J

kg·K ), and T is temperature in Kelvin. Using Eqs. 10 and 11 the air density of air in Oak Ridge, Tennesseewas found to be 1.168×103 g/cm3. This air density does not take into account humidity.

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5.2 Weak Source Corrections

Material Thickness/Distance (cm) Density (g/cm2) MAC ×102cm2/g

Air Varies 1.168*10−3 7.713Water 0.765 1.015 8.574Pyrex 0.06 2.23 7.645

Polyethylene 0.01 0.94 8.807

5.3 Strong Source Corrections

Material Thickness/Distance (cm) Density (g/cm3) MAC ×102cm2/g

Air Varies 1.085×10−3 7.713Iron 0.15 7.874 7.346

6 Analysis and Results

6.1 Weak Source

Distance (m) Uncorrected 1√Rateµ

uncorrected error Corrected 1√Rateµ

corrected error

40.05 0.076272915 0.000169245 0.07636242 0.00016955560.04 0.111097479 0.000357799 0.111350612 0.00035934280.03 0.145670545 0.000614386 0.146104459 0.00061781199.88 0.186688671 0.00100967 0.187201603 0.001013748201.16 0.351237576 0.003564806 0.354367322 0.003630116301.66 0.54641312 0.008639511 0.552562528 0.008821883404.5 0.726856924 0.015383215 0.733526979 0.015543962501.55 0.897324278 0.023010559 0.926465752 0.024797498505.5 0.893831502 0.00420215 0.914903919 0.004411637505.5 0.890674471 0.004168884 0.912467203 0.004388168510.9 0.903917936 0.004286143 0.927895347 0.004537815510.9 0.902077169 0.004273848 0.924891277 0.00450848510.9 0.90371285 0.004302417 0.923756518 0.004497423

100 200 300 400 500Distance

0.2

0.4

0.6

0.8

1

rate

Figure 17: Uncorrected and corrected graph of 1√Rateµ

versus distance

A least square t was performed neglecting the rst point due to dead time (probably pulse pile up). Theslope of the line was calculated to be (179.8±7.5)×10−6, and the intercept was found to be (4.1±0.5)×10−3.This corresponds to a detector face to crystal face distance, r0, of 2.23 cm and a reduced χ2 of 3.65.

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6.2 Strong Source

The weighted average of the strong source was calculated to be 3.415×107 with an uncertainty of 1.975×104.

7 Discussion

The ratio of strong source to weak source as described in equation 8was calculated to be 119.4, and by usingSµ of 34.98 µCi the value of Sm was calculated to be 4.18 mCi and by combining the uncertainty of theweak source guaranteed by NIST (0.70%) with the uncertainty as propagated in experiment (0.46%) thetotal nal error for the experiment was calculated to be 0.84%, as was the goal.

This experiment veries the source strength that was used to calculate the neutron ux was correct, andthe neutron beam intensity is as we have believed. The reliability of the measurement of neutron ux willalso allow for an estimate on the length of time required to achieve an optimum statistical uncertainty.

8 Acknowledgement

This work was supported by NSF award PHY-0855584 and DOE award DE-SC0008107TDD.Special thanks to: C. Crawford, D. Bowman, S. Pentilla, K. Grammer, and Z. Tang.

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References

[1] M. White. The spallation neutron source, August 2002.

[2] SNS ORNL. FNPB- fundamental neutron physics beamline, May 2012.

[3] Monochromator - NPDGamma wiki. http://battlestar.phys.utk.edu/wiki/index.php/Monochromator,February 2010.

[4] P.R. Human, D. Desai, G.L. Greene, P. Koehler, R. Mahurin, G.R. Palmquist, W.M. Snow, and A. Yue.Beamline performance simulations for the fundamental neutron physics beamline, March 2005.

[5] Matthew Musgrave. The NPDGamma experiment and polarimetry using a 3He spin ipper, July 2011.

[6] N. Fomin. Structure of the data stream and possible errors, June 2012.

[7] E. Martin, D. Bowman, S. Balascuta, and Z. Tang. Counting statistics and beam time estimate, August2011.

[8] S. Balascuta, Z. Tang, and D. Bowman. The measurement of the neutron ux at the center of theNPDGamma detector array, July 2011.

[9] J. H. Hubbell and S.M. Seltzer. Tables of x-ray mass attenuation coecients and mass energy-absorptioncoecients, July 2004.

[10] M. J. Berger, J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Suku-mar, D.S. Zucker, and K. Olsen. NIST XCOM: Element/Compound/Mixture.http://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html, July 2012.

[11] NIST. Compositions of materials used in STAR databases. http://physics.nist.gov/cgi-bin/Star/compos.pl?ap.

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