“Scientists peered into the data and concluded that we should all be worried.” ~ Bret Easton Ellis 




Sample Peak Analysis

Here is an example of some of the steps we take during peak analysis:

1. We look for obvious deviations from the continuum in the entire spectrum as well as in predetermined areas
where peaks may be expected. In our soil experiments as we've mentioned, we specifically look for Cesium-
137. Its presence alone can tell us much about the sample and what else to maybe expect to find within the
spectrum. Its major gamma-ray at 661.67 keV is distinct and usually doesn't interfere with other processes that may be producing peaks in that range (usually...good geometry can help reduce that; however, it is possible if Cobalt-60 is present, a single escape peak from an electron flying off can produce a peak where Cesium-137 is found). If it does interfere, we'll have more chances to find out later so first step is find the peak.



1.  We look for obvious deviations from the continuum in 
the entire spectrum as well as in predetermined areas 
where peaks may be expected.  In our soil experiments 
as we've mentioned, we specifically look for Cesium-
137. Its presence alone can tell us much about the sample 
and what else to maybe expect to find within the 
spectrum.  Its major gamma-ray at 661.67 keV is distinct 
and usually doesn't interfere with other processes that 
may be producing peaks in that range (usually...good 
geometry can help reduce that; however, it is possible if 
Cobalt-60 is present, a single escape peak from an 
electron flying off can produce a peak where Cesium-137 
is found).  If it does interfere, we'll have more chances 
to find out later so first step is find the peak.
2.  We'll assume we find one so the next step is to select 

the area it spans, take a quick look at the gross counts 

our program tells us (we could count ourselves each time but it is boring and only needs to be done once to check the program's arithmetic), look at peak shape, 

centroid, etc.  Did it fall within the range it did in prior 

calibrations and tests?  Temperature, humidity, sample 

medium, density, calibration settings, geometry and 

quite a number of other factors can all have affect of 

"shifting" effects of energy peaks on the spectrum.  

While we make great effort in controlling as many of 

these parameters as we can, it is natural to expect this 

to some degree.  In our numerous tests with our check 

sources as well as the experiments with our check source 

in various soils (we know it's not perfect but for 

simulation purposes..), ELA has found that we 

experience a shift up to +/- 1.5 keV under normal 

circumstances specific to Cesium-137's 661.67 keV 

gamma-ray peak.  If it varies too much from this, it'll 

most likely be a conflict with a neighboring peak and/or 

insignificant with respect to background and not 

considered valid.

Another thing we look for at peak selection is the 

standard deviation and having to do with the width of 

the peak and being a function of energy is very important in determining type.  During our calibrations we took note of the standard deviations, estimated the full width half maximum (FWHM) of the peaks whether resulting from gamma-ray interactions, annihilation, x-rays etc.  On the chart below, it is clear that determining this value can be helpful in determining 

source.  Here is how we calculate this along with a  

chart of some of our measurements:
2.  We'll assume we find one so the next step is to select 
the area it spans, take a quick look at the gross counts 
our program tells us (we could count ourselves each time but it is boring and only needs to be done once to check the program's arithmetic), look at peak shape, 
centroid, etc.  Did it fall within the range it did in prior 
calibrations and tests?  Temperature, humidity, sample 
medium, density, calibration settings, geometry and 
quite a number of other factors can all have affect of 
"shifting" effects of energy peaks on the spectrum.  
While we make great effort in controlling as many of 
these parameters as we can, it is natural to expect this 
to some degree.  In our numerous tests with our check 
sources as well as the experiments with our check source 
in various soils (we know it's not perfect but for 
simulation purposes..), ELA has found that we 
experience a shift up to +/- 1.5 keV under normal 
circumstances specific to Cesium-137's 661.67 keV 
gamma-ray peak.  If it varies too much from this, it'll 
most likely be a conflict with a neighboring peak and/or 
insignificant with respect to background and not 
considered valid.
Another thing we look for at peak selection is the 
standard deviation and having to do with the width of 
the peak and being a function of energy is very important in determining type.  During our calibrations we took note of the standard deviations, estimated the full width half maximum (FWHM) of the peaks whether resulting from gamma-ray interactions, annihilation, x-rays etc.  On the chart below, it is clear that determining this value can be helpful in determining 
source.  Here is how we calculate this along with a  
chart of some of our measurements:

2. We'll assume we find one so the next step is to select the area it spans, take a quick look at the gross counts
our program tells us (we could count ourselves each time but it is boring and only needs to be done once to check the program's arithmetic), look at peak shape, centroid, etc. Did it fall within the range it did in prior
calibrations and tests? Temperature, humidity, sample medium, density, calibration settings, geometry and
quite a number of other factors can all have affect of "shifting" effects of energy peaks on the spectrum.
While we make great effort in controlling as many of these parameters as we can, it is natural to expect this
to some degree. In our numerous tests with our check sources as well as the experiments with our check source in various soils (we know it's not perfect but for simulation purposes..), ELA has found that we
experience a shift up to +/- 1.5 keV under normal circumstances specific to Cesium-137's 661.67 keV
gamma-ray peak. If it varies too much from this, it'll most likely be a conflict with a neighboring peak and/or
insignificant with respect to background and not considered valid.


Another thing we look for at peak selection is the standard deviation and having to do with the width of
the peak and being a function of energy is very important in determining type. During our calibrations we took note of the standard deviations, estimated the full width half maximum (FWHM) of the peaks whether resulting from gamma-ray interactions, annihilation, x-rays etc. On the chart below, it is clear that determining this value can be helpful in determining source. Here is how we calculate this along with a chart of some of our measurements:


FWHM = 2√2 log(2)*sd

Notice how, if peaks are not from full energy peaks, the widths at half way up the peak will be wider. The 1173 keV gamma-ray of Cobalt-60 can produce a peak at 662 keV as can Cesium-137's gamma-ray as shown on the chart; however, it is apparent which is which after looking at widths of peaks. 511 keV annihilation peak is another example of a wide peak not caused by a gamma-ray but rather shows the Doppler effect of broadening the peak, or distributing the counts across more channels, as the process of natural reverberation that occurs when a positron hits an electron. Neato! (but not in environmental samples we hope...)


3. So...all of that taken into account, if we find that: A peak is visually present, has over 100 gross counts (so we can apply a normal distribution) within the range of interest, measures within peak centroid and FWHM 

parameters, doesn't require correction for possible summing effects, doesn't conflict with neighboring
peaks, we can then begin the process of proving what our eyes suspected, estimate the area above the background and figure an activity and accordingly assign a confidence level to it. 


ELA wants to know: if we measure this sample 20 more times, will we obtain the same result 19 of those times? That is being 95% confident the estimated value will fall within the range we estimated the first time and is a value in counts that can be determined by calculating the critical limit. It's what the big labs do (or say they do) too so we try to achieve continuity in standards the best we are able. It is this critical limit count value, that
when adjusted for background will determine whether we quote a detection based on that confidence level,
that the value will be within a certain number of standard uncertainties.


Back to our example peak then:

The formula for critical limit for a peak area for 95% confidence is given by:


Lc = 1.645 √[B(1 + (n/2m))]


where B is the corrected background counts, n is the number of channels the peak spans, and m is the number
of channels of backgrounds on one side (although sometimes necessary and possible to adjust for varying m
values, keeping them the same number of channels reduces arithmetic error and is usually not difficult to
achieve without conflict in this range).


In our example, n = 9 channels and each m = 3 channels. B is found by:


B = nS/2m; where S is the sum of the counts in the m background channels, so;

B = (9)(138)/2(3) = 207


Net peak counts is then found by substracting the correction for background from the gross counts,


A = G - B; or A = 43


Is this value "significant"? If it ends up being above the critical limit we will say so. From above:


Lc = 1.645 √[B(1 + (n/2m))]

Lc = 1.645 √ [207(1 + (9/6))]

Lc = 37


Is A > Lc? If yes, the net count is above the critical limit, considered significant, carried through the activity
equation, and posted as a detection with the range of uncertainty from our uncertainty budget.

If it is not, we will then determine the upper limit, or Lu, to find a value we know is just above what the true
value could be and post it as not significant and quote a "less than" number, or Lu. We will post an example of a
situation like this shortly along with how we handle low gross count, or those around <100. If under 100 and
meeting all other requirements of peak detection, it can indicate a bionomial distribution and is treated slightly
differently in calculation. We have noticed this becomes relevant when values hover around Electra's
detection limits in combination with testing time and large background contribution. It is possible to retest and for a longer period of time, but that too introduces uncertainty especially with large background contributions...


We hope that helps explain what we do, until then..:)


*All formulas used above were found in Dr. Gilmore's Practical Gamma-Ray Spectrometry, 2nd edition. If you have the means, we highly recommend picking up a copy. If you do, remember to check his website for possible corrections based on what print you have as some formulas and values were corrected from earlier editions.