# Interpretation of Net Peak Area in Gamma Spectroscopy

• RobotGuy

#### RobotGuy

Hello,

My question relates to gamma spectroscopy. I understand how the net peak area is calculated for any photopeak. Fortunately, gamma-spec software (e.g., Genie-2000 from Canberra) provides Net peak area and associated uncertainty (for Cs-137 661.7 keV peak, as an example). My question: are the values between extremes uniformly distributed? For example, for a hypothetical case with net peak area 1000+/-99, the net peak area can vary between 901 and 1099. So, the values between these extremes are uniformly distributed? In other words, if the experiment is repeated, the probability of getting any peak area between (901,1099) is same? Or is it biased at the centroid (1000)—such that centroid peak area will occur most of the times and the extremes will occur least (like Gaussian nature)?

I am confused because the 'Gaussian Shape' of the photopeak is already accounted to calculate the net peak area?

Thanks,

## Answers and Replies

Hello @RobotGuy ,

No responses so far (perhaps because it is still a bit of a holiday season), so I'll give it a generic shot...

In such software, net peak area and associated uncertainty follow from a fit to an expected profile (Gaussian, Lorenzian or Voigt, possibly on some background function). The uncertainty given is the standard deviation. In your example you may assume a Gaussian distribution centered at 1000 with a sigma of 99.

So definitely not a uniform distribution.

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Hello @BvU ,

That's what I think too. You are right, the uncertainty is standard deviation. What you mentioned can be implemented in Python using random.gauss() function. I also came across this link which simulates that efficiently (and the source is trustworthy too): https://uncertainty.nist.gov/

Mentioned just in case if someone else stops here in the future.

My question: are the values between extremes uniformly distributed? For example, for a hypothetical case with net peak area 1000+/-99, the net peak area can vary between 901 and 1099. So, the values between these extremes are uniformly distributed? In other words, if the experiment is repeated, the probability of getting any peak area between (901,1099) is same? Or is it biased at the centroid (1000)—such that centroid peak area will occur most of the times and the extremes will occur least (like Gaussian nature)?
It's been a long time since I've looked into the details of gamma spectra, but generally, the emission should be a characteristic of the radionuclide. A detector may not receive/detect 'all' of the energy since there is scattering between the source nucleus and the detector, and the scattering is essentially down in energy, not upward. Some of the peak energy is due to the simultaneous detection of a primary (characteristic gamma) and a gamma of lower energy, which is where one would receive a gamma energy > 0.667 keV. The type of detector is also important, e.g., compare spectra from a NaI(Tl) vs Ge(Li) vs LaBr detectors (detector resolution). In the gamma source, gamma rays are emitted isotropically, so one does not necessarily get the full energy of the gamma.
https://en.wikipedia.org/wiki/Gamma_spectroscopy#Interpretation_of_measurements
https://www.ortec-online.com/-/media/ametekortec/brochures/lanthanum.pdf

I am confused because the 'Gaussian Shape' of the photopeak is already accounted to calculate the net peak area?
The 'Gaussian' distribution is a nice approximate (and relatively simple and straightforward) even when distributions are not quite Gaussian.

BvU