Calculation of gamma multiplicities in a multiplying sample for the assay of nuclear materials

Analytical expressions for multiplicities that include induced fission effects have been derived for neutrons in the past. These expressions are given as functions of the probability of induced fission per neutron, and have been investigated both by Monte Carlo methods and in experiments using thermal neutron detectors. The object of this paper is to derive analytical formulae for the multiplicities of the gamma photons emitted by both spontaneous and induced fissions, and to perform a quantitative analysis. In addition, neutron and gamma multiplicities are calculated by Monte Carlo simulation using a modified version of the MCNP-PoliMi code. Good agreement is found between the analytical formulae and the Monte Carlo results. The results show the potential advantage of using gamma multiplicities when compared to neutron multiplicities: their higher quantitative values may, in principle, have the effect of leading to a larger sensitivity on the sample mass when compared to the analysis based on neutrons alone.