Generalized synthetic kernels for neutron slowing down

The validity of classical approximate models describing the elastic slowing down of neutrons in moderating substances is analyzed in terms of the approximation of analytic functions in the complex plane. The synthetic models of Fermi, Wigner and Greuling-Goertzel which were introduced by pure physical reasoning are shown to be related to first-order Padé approximants of the true slowing down kernel. This formalism is easily extended to higher orders ; care must be taken, however, to avoid " unphysical " models which might arise if, for instance, the inequality [formule] — with [formule], the Laplace transform of the approximate slowing down kernel — were satisfied at some points lying in the right-half complex plane. Use is made of the requirement Re [formule] everywhere in [formule], together with a classical interpolation algorithm in the unit disk to obtain an entirely new family of approximate kernels which are shown to give quite accurate results in some elementary situations.Mund Ernest H., Van Binnebeek J. J. Generalized synthetic kernels for neutron slowing down. In: Bulletin de la Classe des sciences, tome 62, 1976. pp. 289-311