Moments of the Neutron Time‐Energy Distribution and the Use of Random Functionals

The time moments of the neutron time‐energy distribution are derived under the following conditions: infinite homogeneous moderator with no absorption, elastic scattering, and distribution of scattering angle independent of energy in center‐of‐mass frame. However, no assumption is made on the variation of the scattering cross section with energy. This is in contrast to previous papers in which a scattering cross section proportional to v δ (δ any real number) is assumed. The moments are derived in two ways: first, by means of Laplace transforms, and then through the use of random functionals. Random functionals have not been previously employed in neutron moderation theory and they offer certain advantages which are discussed.