Statistical precision of delayed-neutron nondestructive assay techniques

Abstract

A theoretical analysis of the statistical precision of delayed-neutron nondestructive assay instruments is presented. Such instruments measure the fissile content of nuclear fuel samples by neutron irradiation and delayed-neutron detection. The precision of these techniques is limited by the statistical nature of the nuclear decay process, but the precision can be optimized by proper selection of system operating parameters. Our method is a three-part analysis. We first present differential--difference equations describing the fundamental physics of the measurements. We then derive and present complete analytical solutions to these equations. Final equations governing the expected number and variance of delayed-neutron counts were computer programmed to calculate the relative statistical precision of specific system operating parameters. Our results show that Poisson statistics do not govern the number of counts accumulated in multiple irradiation-count cycles and that, in general, maximum count precision does not correspond with maximum count as first expected. Covariance between the counts of individual cycles must be considered in determining the optimum number of irradiation-count cycles and the optimum irradiation-to-count time ratio. For the assay system in use at ORNL, covariance effects are small, but for systems with short irradiation-to-count transition times, covariance effects force the optimum number of irradiation-count cycles to be half those giving maximum count. We conclude that the equations governing the expected value and variance of delayed-neutron counts have been derived in closed form. These have been computerized and can be used to select optimum operating parameters for delayed-neutron assay devices.