Yasunori Yamamura

An Improvement to the G. G. Approximation in Neutron Slowing Down through the Method of Generalized Function

The neutron slowing down problem in an infinite homogeneous medium is treated within the G.G. approximation through the theory of generalized function (g.f.). As test function for defining the g.f.s, the source importance for the slowing down is chosen. In place of the Taylor expansion of the collision term of slowing down equation in the G.G. method we expand the adjoint collision term of the importance equation. Solutions obtained with this method clearly reproduce the Placzek wiggles, which do not appear in corresponding solutions by the orthodox G.G. method using the same order of approximation, and our solutions are in very good agreement with the exact Placzek function.

Analytical Study of the Effect of Anisotropic Scattering in C. M. S. on Fast Neutron Spectrum

With use made of the synthetic scattering kernel presented in a previous paper a simple analytic formula for the neutron slowing down spectrum is obtained within the order of the G.G. approximation under the condition that the elastic scattering is anisotropic in the center of mass system (c.m.s.). In the formula thus derived the Legendre expansion coefficient of the scattering angular distribution is included explicity in the form of arbitrary functions of energy. Scattering and absorption cross sections are also treated as arbitrary functions of energy. Collorary information deriving directly from the formula obtained, such as resonance escape probability and the effect of finite buckling are discussed.

Wigner-type continuous slowing down theory for the fast-neutron spectrum

The Wigner-type continuous slowing down theory is derived from the physical point of view, considering the neutron balance in lethargy space, and is applied to the calculation of neutron spectra in fast-reactor compositions, where the moderating effect of inelastic scattering is very important. The present theory corresponds to the macroscopic representation of the moderating process of neutrons.

Some Remarks on the Greuling Goertzel Approximation for the Higher PL Equation

The Greuling Goertzel approximation is often used in reactor physics for the simplicity of its equations and the consequent ease of their solution. Eversince the original theory was presented by Greuling et al.(1), many authors have developed this formalism to accommodate anisotropic scattering and scattering angular distribution. The Greuling Goertzel approximation was successfully used for the calculation of reactor parameters and fluxes in a thermal reactor assembly, of which the cross sections vary slowly with energy. Later, Segev(2), Dunn & Becker(3) and Stacey(4) have demonstrated that the modified Greuling Goertzel approximation can be applied to the treatment of the elastic moderation of neutrons in a fast reactor assembly, where strong scattering resonance are prevalent. The aim of the present note is to point out that the ordinary Greuling Goertzel approximation for the higher PL approximation derived by Amster(5) and Ferziger & Zweifel(6), may yield unstable and unreasonable solutions. Generalized derivations of the Greuling Goertzel theory were presented by the same Amster, Ferziger & Zweifel and by Williams(7). The notations used here are same as those of Ferziger & Zweifel. The final form of the PL-equation modified by the Greuling Goertzel approximation takes the form(6)