# Gamma spectrometry

I want to calculate minimum detectable activity (MDA) at 200 and 300 keV energy of a gamma spectrometry by HPGe detector. 662 keV Photopeak is present for 137Cs.

Assume 2 scenarios:

1. There is a 'peak' at 200 keV. Let's say net counts is 'b' unit. And gross count is 'a+b' unit.
2. There is no peak at 300 keV. Gross count is 'c' unit

Using Curie's formula, we can calculate MDA.

What background value $$B$$ should I use in the above cases?

Pl see the image.

• With such Gamma ray spectroscopy you'd be dealing with counts not area. The detection limit would depend on what else in the sample was emitting gamma rays and hence raising the background counts (noise). Another gamma ray near 662 keV would result in peak overlap and substantially increase the background noise. – MaxW Jul 23 '19 at 4:40
• @ggs Can you take a minute and explain this a little more clearly? I've added some formatting to your question but I think you can explain more systematically. Also, what is Curie's formula? There is Curie's law but that's a horse of a different color. – uhoh Jul 23 '19 at 5:32

The Currie algorithm* for the calculation of the minimum detectable activity (MDA) is generally considered obsolete. Today, detection limits are calculated according to ISO 11929 and related standards (for example, see also https://chemistry.meta.stackexchange.com/a/3283/7951)

Nevertheless, when using the Currie MDA algorithm, the detection limit $$L_\mathrm D$$ is calculated using $$L_\mathrm D=k^2+2L_\mathrm C$$ which can be translated into MDA.

In calculating the detection limit, the continuum is based on data on each side of the peak region for peaks that were found. It is based on the equivalent of the peak region itself for peaks that were not found.

For example, for a found peak with the linear continuum model in effect (ypou could also use a step continuum model instead), the continuum is calculated as $$B=\left(\frac N{2n}\right)\left(B_1+B_2\right)$$ Where
$$N$$ is the number of channels in the peak region,
$$n$$ is the number of channels on each side of the peak region used for the determination of the continuum counts,
$$B_1$$ is the sum of counts in the $$n$$ channels to the left of the peak region, and
$$B_2$$ is the sum of counts in the $$n$$ channels to the right of the peak region.

For peaks that had a background interference component subtracted, the equation for $$L_\mathrm C$$ becomes $$L_\mathrm C=k\sqrt{B+\left(\frac{T_\mathrm s}{T_\mathrm b}I_\mathrm b\right)+\left(\frac N{2n}\right)^2\left(B_1+B_2\right)+\left(\frac{T_\mathrm s}{T_\mathrm b}\right)^2\sigma_{I_\mathrm b}^2}$$ Where
$$B$$ is the value of the continuum subtracted,
$$I_\mathrm b$$ is net peak area of the background measurement,
$$T_\mathrm s$$ is the live time of the sample measurement, and
$$T_\mathrm b$$ is the live time of the separate background measurement.

This equation is used as a critical level test criterion, for example at $$95\ \%$$ confidence level. If the net peak area is less than $$L_\mathrm C$$, then a “not detected” decision is made. If the net peak area is greater than $$L_\mathrm C$$, then a “detected” decision is made.