Draft:Minimum detectable activity

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

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

where $L_{D}$ ins the detection limit in units of counts, $\epsilon _{\gamma }$ is the detection efficiency of the gamma spectrometer at the particular gamma-ray energy, $P_{\gamma }$ 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%,

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

where $\sigma _{0}$ 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 $\sigma _{0}={\sqrt {2B}}$.