Abstract
Eigenvalue problem in time and space dependent thermalization transport equation are summarized. They are important in analysis of time decay constant λ and diiffusion length 1/κ measurements. A study of the Wigner-Wilkins type differential equation for the proton gas moderator indicates the existence of an infinite number of discrete time dependent eigenvalue λκ in the range 0≤λκ<(υΣ)min and of a continuous eigenvalue λ in the range (υΣ)min<λ which has a singular eigenfunction. A method of singular integral equation developed by Muskhelishvili is used in order to prove the existence of the singular eigenfunction in the case of more general scattering kernel. They are compared with a expansion method of a flux in terms of polynomials of energy or of velocity. A boundness of time eigenvalues of infinite and finite medium are illustrated for the both cases of mono energetic neutron and thermalizing neutron. The relevance of Boltzmann transport equation is studied for the very slow neutron. Finally the discussion of the spacial eigenvalue problem is added.
