[en] Using passive thermal neutron coincidence counting techniques, the accuracy of nondestructive assays of fertile material can be improved significantly using a two-ring detector. It was shown how the use of a function of the coincidence count rate ring-ratio can provide a detector response rate that is independent of variations in neutron detection efficiency caused by varying sample moderation. Furthermore, the correction for multiplication caused by SF- and (α,n)-neutrons is shown to be separable into the product of a function of the effective mass of ²⁴⁰Pu (plutonium correction) and a function of the (α,n) reaction probability (matrix correction). The matrix correction is described by a function of the singles count rate ring-ratio. This correction factor is empirically observed to be identical for any combination of PuO₂ powder and matrix materials SiO₂ and MgO because of the similar relation of the (α,n)-Q value and (α,n)-reaction cross section among these matrix nuclei. However the matrix correction expression is expected to be different for matrix materials such as Na, Al, and/or Li. Nevertheless, it should be recognized that for comparison measurements among samples of similar matrix content, it is expected that some function of the singles count rate ring-ratio can be defined to account for variations in the matrix correction due to differences in the intimacy of mixture among the samples. Furthermore the magnitude of this singles count rate ring-ratio serves to identify the contaminant generating the (α,n)-neutrons. Such information is useful in process control