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

Abstract 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 ( P 0 ) and first ( P 1 ) 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.