B\uf6hnel multiplicity formulae beyond the point model

Passive methods of nuclear safeguards determine the important parameters of an unknown sample from the statistics of the detection of the neutrons emitted from the item. These latter are mostly due to spontaneus fissions (and (α,n) reactions, neglected here), enhanced by a slight internal multiplication before leaking out. Following the original work of B\uf6hnel [1], the methodology of traditional multiplicity counting is based on the first three factorial moments of the number of neutrons, emitted from the sample due to one source event. These “B\uf6hnel moments” were derived in the so-called “point model”, in which no space-dependence is assumed, rather a uniform first collision probability is assumed for each neutron, irrespective of the position of its birth and its velocity direction. The purpose of the present work is to derive the same factorial moments in a one-speed space-dependent model, in which the position and direction of the neutrons is accounted for, but (similarly to the original B\uf6hnel model), no energy dependence is assumed