Transport Theory of Neutron Wave Propagation by Eigenfunction Expansion Method

Abstract

An eigenfunction expansion method is developed for the neutron wave propagation theory with a cut off cross section. The full and half range orthogonality relations for the eigenfunctions are derived, which are respectively applied to obtain an infinite space solution and the space eigenvalue formula.
The formula is tried on some actual evaluations, and found to reduce considerably the laborious procedure required hitherto. The existence of marked interference phenomena between the discrete and the pseudo modes is demonstrated by numerical calculations performed on the solutions for graphite and beryllium.