Neutron escape probabilities in 3-D reentrant geometries computed using ray tracing

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Escape probabilities are fundamental inputs in the calculation of self-shielded cross sections for multigroup neutron transport models. Rational approximations are often used to compute escape probabilities in geometries commonly encountered in nuclear reactors. Although analytical approximations are simple and rapid, they are limited in applicability and accuracy. Here we show that ray tracing can be used to compute accurate escape probabilities in reentrant geometries with and without spherical symmetry. We use 3-D ray tracing to compute escape probabilities and their uncertainties in a spherical shell with a central void and a six-pointed cross shape. Results are benchmarked by comparison to Monte Carlo neutron transport simulations done in MCNP6.2 and analytical results. The escape probabilities in the spherical shell computed with ray tracing are within 0.51% of the analytical benchmark, and in the cross geometry the escape probabilities are within 1.4% of the MCNP6.2 benchmark.