The neutron-gamma Feynman variance to mean approach: Gamma detection and total neutron-gamma detection (theory and practice)

Two versions of the neutron gamma variance to mean (Feynman-alpha method or Feynman-Y function) formula for either gamma detection only or total neutron gamma detection, respectively, are derived and compared in this paper. The new formulas have particular importance for detectors of either gamma photons or deleclors sensitive to both neutron and gamma radialion. If applied to a plastic or liquid deleclor, he total neutron-gamma detection Feynman-Y expression corresponds Lo a situation where no discrimination is made between neutrons and gamma parlicles. The gamma variance Lo mean formulas are useful when a detector of only gamma radialion is used or when working with a combined neutron-gamma deleclor at high count rates. The theoretical derivation is based on the Chapman-Kolmogorov equation with the inclusion of general reactions and corresponding intensities for neutrons and gammas, but with the inclusion of prompt reactions only. A one energy group approximation is considered. The comparison of the two different theories is made by using reaction intensities obtained in MCNPX simulations with a simplified geometry for two scintillation detectors and a Cf-252-source. In addition, the variance to mean ratios, neutron, gamma and total neutron-gamma are evaluated experimentally for a weak Cf-252 neutron-gamma source, a Cs-137 random gamma source and a Na-22 correlated gamma source. Due to the focus being on the possibility of using neutron-gamma variance to mean theories for both reactor and safeguards applications, we limited the present study to the general analytical expressions for Feynman-alpha formulas