The Nuclear Detection Figure Of Merit (NDFOM) portal is a database of objects and algorithms for evaluating the performance of radiation detectors to detect nuclear material. This paper describes the algorithms used to model the physics and mathematics of radiation detection. As a first-principles end-to-end analysis system, it starts with the representation of the gamma and neutron spectral fluxes, which are computed with the particle and radiation transport code MCNPX. The gamma spectra emitted by uranium, plutonium, and several other materials of interest are described. The impact of shielding and other intervening material is computed by the method of build-up factors. The interaction of radiation with the detector material is computed by a detector response function approach. The construction of detector response function matrices based on MCNPX simulation runs is described in detail. Neutron fluxes are represented in a three group formulation to treat differences in detector sensitivities to thermal, epithermal, and fast neutrons
