The Theory of Neutron Wave Propagation

Abstract

The objectives of this thesis include the development of an exact theory of neutron wave propagation in non-multiplying media as well as the application of this theory to analyze current experimental work.

An initial study is made of the eigenvalue spectrum of the velocity-dependent Boltzmann transport operator for plane wave propagation in both noncrystalline and polycrystalline moderators. The point spectrum is discussed in detail, and a theorem concerning the existence of discrete eigenvalues for high frequency, high absorption, and/or small transverse dimensions is demonstrated. The limiting cases of low and high frequency behavior are analyzed. A physical interpretation of the discrete and continuum eigenfunctions (plane wave modes) is given, and the point spectrum existence theorem is explained in the light of such interpretations.

Using this spectral representation, a technique for solving full-range boundary value problems for a general noncrystalline scattering kernel is presented. Orthogonality and completeness of the eigenfunctions are demonstrated, and the problem of a plane source at the origin of an infinite medium is solved. This solution is compared with that obtained by a Fourier transform technique. A procedure for solving half-range boundary value problems is presented for a one-term separable kernel model. For purposes of illustration, the problem of an oscillating source incident upon the boundary of a half-space is solved. The difficulty in extending the half-range theory to more general scattering models is discussed.

The second part of the thesis proceeds to demonstrate this theory in more detail by applying it to analyze recent neutron wave experiments in graphite and D2O parallelepipeds. To facilitate the interpretation of the general solution, the inelastic scattering kernel is approximated by a separable kernel, while the elastic scattering is modeled with a Dirac delta-function. The eigenvalue spectrum in analyzed in some detail, revealing several interesting conclusions concerning the experimental data and methods of data analysis. Several modifications in experimental design and analysis are suggested.

The agreement of the theory with experiment is sufficient to warrant its application to the analysis of more complicated experiments (multiple-region, multiplying media, pulse propagation, etc.). Several suggestions for such extensions are indicated.