On the role of the detection process in the performance of the neutron-gamma Feynman variance-to-mean approach

The investigations of the asymptotic values of Feynman-Y functions for gamma and total (neutron + gamma) detections [1] indicated a substantial deviation between theory and exper- iment. The difference highlights the fundamental importance of accounting for the underlying physical process of detection for correct estimation of theoretical and experimental values of the source activity. We suppose that there are two main aspects associated to the problem. First, the theoretical approach [1, 10] of the detection process assumes the removal of the de- tected particle from the process. This is generally correct for some types of detectors, e.g. 3He-counters of thermal neutrons where a 3He(n,p)3H reaction takes place. However, consider- ing liquid scintillation detectors, the same particle can be multiply detected, since it undergoes elastic scattering (neutrons) and Compton scattering (gammas) to be detected and therefore, a detection does not necessarily remove it from the process. Second, in the case of gamma detection, the importance of cascade gammas and the way the detector resolution affects the results is not yet clear. Therefore, to shed some light on this question, in this paper we undertake a theoretical investigation of these aspects. The theoretical work is aimed at the derivation of a new version of the neutron-gamma Feynman variance-to-mean approach where particles are not necessarily removed from the process after a first detection. This paper reports on the results of both theoretical and numerical investigations.