Comparison of the Wilkins Equation and Higher Order Approximations for Solid Moderators

Approximations to the Boltzmann equation including the first two terms in the inverse mass expansion are developed for anisotropic moderators. An asymptotic solution is obtained. The results for beryllium and graphite are compared with the results of the Wilkins approximation. It is seen that this approximation constitutes an improvement over the Wigner and Wilkins gaseous model because the error produced by neglecting higher orders in the inverse mass expansion is in the right direction to account for crystalline binding.