Convergence of Legendre Expansion of Doppler-Broadened Double Differential Elastic Scattering Cross Section

Convergence properties of Legendre expansion of a Doppler-broadened double-differential elastic neutron scattering cross section of 238U near the 6.67 eV resonance at temperature 103 K are studied. A variance of Legendre expansion from a reference Monte Carlo computation is used as a measure of convergence and is computed for as many as 15 terms in the Legendre expansion. When the outgoing energy equals the incoming energy, it is found that the Legendre expansion converges very slowly. Therefore, a supplementary method of computing many higher-order terms is suggested and employed for this special case.