Draft:Minimum detectable activity

{{Short description|Measurement concept in nuclear physics}}

{{Draft topics|mathematics}}

{{AfC topic|stem}}

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{{AfC submission/draft}}

Minimum detectable activity (MDA) is the lowest activity of a radioactive nuclide that can be detected with a detector system, given a particular confidence level{{cite book |last1=Gilmore |first1=Gordon |title=Practical gamma-ray spectrometry |date=2011 |publisher=Wiley |location=Chichester |isbn=978-0-470-86196-7 |edition=2., repr. with corr}}. It is a concept that can be used in several circumstances, such as in whole-body counting or monitoring atmospheric radionuclides{{cite journal |last1=Britton |first1=R. |last2=Davies |first2=A. V. |last3=Burnett |first3=J. L. |last4=Jackson |first4=M. J. |title=A high-efficiency HPGe coincidence system for environmental analysis |journal=Journal of Environmental Radioactivity |date=1 August 2015 |volume=146 |pages=1–5 |doi=10.1016/j.jenvrad.2015.03.033 |url=http://dx.doi.org/10.1016/j.jenvrad.2015.03.033 |issn=0265-931X}}, to determine the presence or absence of a radioactive substance or compare the performance of detector systems.

When it comes to gamma spectroscopy, the minimum detectable activity can be written as

$MDA\; =\; \backslash frac\{L\_D\}\{\backslash epsilon\_\backslash gamma\; \backslash cdot\; P\_\backslash gamma\; \backslash cdot\; t\_M\}$,

where $L\_D$ ins the detection limit in units of counts, $\backslash epsilon\_\backslash gamma$ is the detection efficiency of the gamma spectrometer at the particular gamma-ray energy, $P\_\backslash gamma$ is the probability of emission for the gamma ray, and $t\_M$ is the live time of the measurement. The formula for $L\_D$ changes depending on the confidence level. For a confidence level of 95%,

$L\_D\; =\; 2.71\; +\; 3.29\; \backslash sigma\_0$,

where $\backslash sigma\_0$ is the uncertainty in background counts in a region-of-interest around the ramma-ray energy. If $B$ is the number of background counts in the region-of-interest, it can be shown that $\backslash sigma\_0\; =\; \backslash sqrt\{2B\}$.