Computation of the Doppler-broadened scattering kernel and its Legendre moments

A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, without making assumptions on the variation of the cross section with energy and for a general scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing for a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented.