The solution of the time-independent neutron slowing down equation using a numerical laplace transform inversion

The transport equation describing steady state neutron slowing down in an infinite medium with constant cross sections is solved numerically using a recently developed numerical Laplace transform inversion algorithm. The basis for the algorithm (described below) is an evaluation of the Bromwich integral without analytical continuation. This method of evaluation avoids the requirement of determining the singularities of the transform in detail and readily allows consideration of scattering from multiple species when constant cross sections are assumed.