The joint distribution of neutrons and gamma photons from fissile samples and its application in safeguards

In this paper the theory of the joint neutron-gamma photon distributions emitted from fissile samples with an intrinsic neutron source, i.e. spontaneous fission, is described. In a sample of finite size short fission chains will develop for each initial source event, thereby changing the number distributions (multiplicities) of the emitted neutrons and gamma photons as compared to the elementary source events. Although in the fission process the neutrons and the gamma photons are generated independently of each other, since new gamma photons are also generated in the fission chain, the number of total emitted neutrons and gamma photons will develop correlations which increase with increasing sample mass. In the paper the general theory of the joint distributions is derived through master equations for the generating functions. The first few joint factorial moments are calculated explicitly, including the covariance between the neutron and gamma photon numbers.