Lab 1 • Become familiar with apparatus and use• Calibrate the energy scale of the detector• Measure the efficiency of the detector• Measure radiation vs detector/source separation and

compare to models• Background Subtraction. Record spectrum with 60 Co

source, with no source, subtract.

Lab 1 • Calibrate the energy scale of the detector

See Python Example for Orthogonal Distance Regression Fit

Lab 1 • Measure the efficiency of the detector

Source Activity (when new)Half-lifeDate created

Detector3” diameterDistance r from source

𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 =𝑑𝑑𝑒𝑒𝑑𝑑𝑒𝑒𝑒𝑒𝑑𝑑𝑒𝑒𝑑𝑑𝑒𝑒𝑑𝑑/𝑢𝑢𝑒𝑒𝑒𝑒𝑑𝑑_𝑑𝑑𝑒𝑒𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑑𝑑𝑒𝑒𝑒𝑒𝑑𝑑/𝑢𝑢𝑒𝑒𝑒𝑒𝑑𝑑_𝑑𝑑𝑒𝑒𝑡𝑡𝑒𝑒

Do Not copy this diagram for your report. Make your own!

Lab 1 • Measure radiation vs detector/source separation and

compare to models (compare models, see lab handout)

See Python Examples for Orthogonal Distance Regression Fit

Lab 1 • Background Subtraction. Record spectrum with 60CO

source, with no source, subtract.

Source 137CS

No Source

Difference

See Python Example for Background Subtraction

But how do I get the errors?

Error in Number of Net Counts, ie number of counts above background?A reasonable estimate is the square root of the number of total (gross) counts. The MAESTRO software “peak information” provides a more sophisticated estimate, see equation 21, p79 of manual.

Error in gamma energy emitted from a source?These are known to much higher precision than the other errors in your lab. You can assume the error is negligible, use a very small error in your data file.

Region of Interest (ROI)

Gross Counts are the total counts in the ROI

Net Counts are the counts in the peak region(Gross-Background)

Adapted from figure 61, p 70 of Ortec MAESTRO manual

But how do I get the errors?Error in Number of Net Counts, ie number of counts above background?A reasonable estimate is the square root of the number of total (gross) counts. The MAESTRO software “peak information” provides a more sophisticated estimate, see equation 21, p79 of manual, which yields a somewhat larger estimate. Available on course website.

Error in gamma energy emitted from a source?These energies are typically known to much higher precision than the other errors in your lab. You can assume this error is negligible, use a very small error in your data file.

Error on mean of peak distribution?

it is NOT one 1 binit is NOT the σ of the distribution

Does depend on how many counts are in the peakmore counts means smoother distribution, smaller error

ANS: = σ𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝑵𝑵

where N is the number of net counts

How do I get σ? Full Width at Half Maximum (FWHM) is reported by MAESTRO. FWHM is exactly what it says it is. For a Gaussian Distribution FWHM = 2.35σ

For explanation, see next slides

Signal Size (bin #)

Num

ber o

f Pul

ses(

Sign

al S

ize)

Signal Size (bin #)

Num

ber o

f Pul

ses(

Sign

al S

ize)

x x xx

x xxx

x xx

xxx x xx

x xx

x

xx

xxx x

x

Same sigma, small NMean is known less precisely

Same sigma, big NMean is known more precisely

∂f∂u( )2 ∂f

∂v( )2 ∂f∂w( )2

recall error analysis from adlab 1:suppose some measurement x that depends on u,v,w:x = f(u,v,w) with errors σu,σv,σw

σx2 = σu

2. + σv2. + σw

2.

X =i=1

N 1N Xi

.

Derivation of Statistical Uncertainty on Mean

Xi=1

N 1N Xi∂xi

∂∂xi

∂ ( ) = 1N

=σx2 =

i=1

N σi

2( )2∂x∂xi

σx2 =

i=1

N σi

2( )21N N

= σ2 σx =N

σ

Apply this to the equation for the mean:

FWHM: Full Width Half Maximum

From FWHM, one can deduce the σ of the given distribution that fits the data best.

As, most of the time, one can fit the data with a Gaussian distribution FWHM = Γ = 2.354 . σ

In practice, one need to determine σ “experimentally” from a set of data (measurements).

Easy way to do it: FWHM (Full Width at Half Maximum).