Analytic evaluation of hydrogen neutron elastic scattering moments with free-gas thermal treatment compared to NJOY

In this paper, we present an analytic approach to evaluate Legendre moments of hydrogen neutron elastic scattering differential cross section, with and without free-gas thermal treatment. The results for the zero-th (P0) and first (P1) moments are given and compared against a 138-group cross sections produced by NJOY. An MCNP thin-wire test was employed as an independent verification for our analytic model for the free-gas zero-th moment. Excellent agreement was observed between the analytic result and MCNP prediction. They both suggest that an increased thermal cut-off in NJOY THERMR module is advisable for higher accuracy. Discrepancy was also found between the analytic model and NJOY multi-group cross section for the first order Legendre moments of the differential cross section, which might indicate a numerical anomaly in NJOY. •Analytic expression for energy transfer of neutron scattering cross section moments is derived from two-body kinematics.•Comparison were made between analytic model, NJOY generated multi-group and continuous energy cross sections.•Hard-coded limit in NJOY thermal treatment cut-off was discovered and its impact on simulation accuracy was illustrated.