Draft:Minimum detectable activity

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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^[1]. It is a concept that can be used in several circumstances, such as in whole-body counting or monitoring atmospheric radionuclides^[2], 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

${\displaystyle MDA={\frac {L_{D}}{\epsilon _{\gamma }\cdot P_{\gamma }\cdot t_{M}}}}$,

where ${\displaystyle L_{D}}$ ins the detection limit in units of counts, ${\displaystyle \epsilon _{\gamma }}$ is the detection efficiency of the gamma spectrometer at the particular gamma-ray energy, ${\displaystyle P_{\gamma }}$ is the probability of emission for the gamma ray, and ${\displaystyle t_{M}}$ is the live time of the measurement^[1]. The formula for ${\displaystyle L_{D}}$ changes depending on the confidence level. For a confidence level of 95%,

${\displaystyle L_{D}=2.71+3.29\sigma _{0}}$,

where ${\displaystyle \sigma _{0}}$ is the uncertainty in background counts in a region-of-interest around the ramma-ray energy. If ${\displaystyle B}$ is the number of background counts in the region-of-interest, it can be shown that ${\displaystyle \sigma _{0}={\sqrt {2B}}}$^[1].