Spectrum calculations for neutrons slowing down by elastic collisions

Abstract

A method is suggested for obtaining the collision density as a function of lethargy for neutrons slowing down in an infinite homogeneous moderator containing uniformly distributed sources of fission neutrons. The only reactions considered are elastic scattering, spherically symmetric in the centre of mass system and absorption. The solution, which is exact for single element moderators when the only neutron reaction is elastic scattering, extends the well known. Greuling-Goertzel approximation and shows that it is in error by no more than 13 per cent. The method is also exact for a mixture of nuclides, provided the cross section ratios are energy independent, and a useful approximation otherwise.