Variational Estimates of Neutron-Induced Gamma Line Leakages and Ratios for Internal Interface Perturbations

Standard variational estimates for perturbations in inhomogeneous transport problems were applied to internal-interface perturbations in coupled neutron-photon problems. Absolute gamma-ray line leakages and ratios of line leakages were the quantities of interest. Gamma-ray spectroscopy using the deterministic multigroup discrete-ordinates code PARTISN was accomplished with a 130-group neutron library and a 120-group photon library with narrow bins centered around gamma lines of interest. Perturbed integrals were evaluated using a volume and a surface formulation, and issues involving negative fluxes (required in the adjoint calculation for line ratios) were addressed. Numerical test problems used a ²⁵²Cf source surrounded by a material containing nitrogen and hydrogen; the thickness of this material was perturbed ±86%. The ratios of the 1.8848-, 2.2246-, and 5.2692-MeV thermal neutron capture lines were very well estimated using the variational estimates, even for macroscopic-size perturbations of internal interface locations; the volume-integral formulation for the perturbed integrals was generally more accurate than the surface-integral formulation for estimating ratios. For estimating absolute leakages, the Roussopolos functional in the surface-integral formulation was clearly superior when the gamma-producing shell was thickened, but it produced negative estimates when the shell was thinned.