Surface and Volume Integrals of Uncollided Adjoint Fluxes and Forward-Adjoint Flux Products

Ray analysis techniques are standard for computing the uncollided component of a detector response to radiation. In this paper, uncollided adjoint flux integrals and forward-adjoint inner product integrals in volumes and on surfaces are derived for general geometries. In numerical test problems using a one-dimensional sphere and a two-dimensional (r-z) cylinder, deterministic and stochastic evaluations of the integrals yielded the same results. A semianalytic benchmark for the adjoint flux integral on a cylindrical surface is also used.