Neutron coincidence measurements when nuclear parameters vary during the multiplication process

Abstract

In a recent paper, a physical/mathematical model was developed for neutron coincidence counting, taking explicit account of neutron absorption and leakage, and using dual probability generating function to derive explicit formulae for the single and multiple count-rates in terms of the physical parameters of the system. The results of this modeling proved very successful in a number of cases in which the system parameters (neutron reaction cross-sections, detection probabilities, etc.) remained the same at the various stages of the process (i.e. from collision to collision). However, there are practical circumstances in which such system parameters change from collision to collision, and it is necessary to accommodate these, too, in a general theory, applicable to such situations. For instance, in the case of the neutron coincidence collar (NCC), the parameters for the initial, spontaneous fission neutrons, are not the same as those for the succeeding induced fission neutrons, and similar situations can be envisaged for certain other experimental configurations. This present document shows how the previous considerations can be elaborated to embrace these more general requirements.