Neutron elastic scattering kernel for Monte Carlo next-event estimators in Tripoli-4®

This paper presents the implementation and the numerical validation of the exponential track length estimator (eTLE) for neutron transport in Tripoli-4((R)). The eTLE is a next-event estimator (NEE), which has the aim of doing variance reduction when paired with a forced-flight method. Like any other NEE, it hinges on deterministic transport through volumes with an attenuation factor applied to the particle's weight. The application of NEEs to neutron-transport problems is impeded by the treatment of Doppler broadening. Indeed, the free-gas thermal treatment complicates the kinematic laws and changes the scattering probability, compared with an isotope at rest. Moreover, in crystalline materials, coherent elastic scattering is on the surface incompatible with NEEs due to its discrete angle scattering distribution. Because certain of the scattering angles are forbidden by the nature of the discrete distribution, and because NEEs are weighted by the differential scattering probability, the naive implementation of the NEE is biased. The paper surveys the evaluation of this quantity for the free-gas thermal treatment and for the coherent elastic scattering. Results to validate the implementations are benchmarked on a simple configuration against the classical unbiased track-length estimator (TLE) for several scattering nuclei and moderators.