Equivalence of Taylor series approximation with transcendental equation of neutron slowing down theory under constant cross sections

Neutron moderation in an infinite homogeneous medium with constant cross sections, which is traditionally treated by Taylor series approximation methods, bears a close correspondence with the exact transcendental equation approach, as has been demonstrated by reducing the exact result to approximate forms. In this paper we give an alternative approach in which the convergence of the approximations to the exact result is derived by allowing the order of approximation to increase indefinitely. The approach is based on the fact that the usual approximations do not give a self consistent definition of the effective mass parameter. The present result can hence be considered as the slowing down counterpart of Davison's treatment of the one speed equation in the Psub(l) approximation. (auth.)