Neutron slowing and thermalization in atomic hydrogen gas

The neutron spectrum resulting from a monoenergetic source in an infinite medium, composed of atomic hydrogen gas and a 1/v absorber, is evaluated by series methods applied to integral and differential equations. The properties of the series that make up a fundamental set of solutions are examined. The classic analysis of Wigner and Wilkins is extended by determining the Green's function for thermalization, a new interpretation is provided for the relationship of asymptotic and small argument series, and calculations are reported for a variety of physical situations.