Electrical and Computer Engineering ETDs

Publication Date

3-21-1966

Abstract

One of the most useful approaches for gaining understanding of atomic structure is that of experiments involving electron scattering from atoms. In particular, knowledgle of differential and total elastic scattering cross sections enables one to calculate momentum transfer cross sections, mean free path, and the width of multiple scattering distributions. From the point of view of a theorist, the central question is that of the interaction potential. A representation of this latter quantity will give rise, mathematically, to a two point boundary value problem involving the Schrödinger equation. Upon solving the Schrodinger equation, and satisfying the appropriate boundary con­ditions, the solutions will contain quantities called phase shifts, which are intimately connected with the given representation of the interaction potential. Knowledge of the phase shifts enables one to calculate the differential scattering cross section and all of the other quantities referred to above. Further, knowledge of the potential enables one to calculate such widely diverse quantities as X-ray form factors, and atomic susceptibilities.

In this dissertation, we shall be concerned with the question of potential representation and the differences which various potentials cause in the calculation of phase shifts. For the most part, spherically symmetric potentials will be discussed, although there is a self-contained section on the subject of calculating non-spherically symmetric potentials. We shall calculate phase shifts for electron scattering in a range of incident electron energies such that Ooo the first Bohr radius of hydrogen. Specifically, the method will be based on numerical solutions of the so-called Franchetti equation for determination of the phase shifts. Having the phase shifts, we can then calculate differential elastic scattering, total elastic scattering, and momentum transfer cross sections.  This will be done for a few selected elements. Parenthetically, it should be added that the lack of adequate computing facilities has necessitated a severe restriction on the amount of data given in this dissertation. For example certain of our calculations involving a single element, with a fixed electron energy. and a fixed angular momentum, have required hours of IBM 1620 time. A higher speed data pro­cessing unit could have performed the same calculation in a few minutes. Certain of the calculations were performed at the Los Alamos Scientific Laboratories, on an IBM 7094 data processing unit.

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

William Jackson Byatt

Second Committee Member

Wayne Willis Grannemann

Third Committee Member

Harold Dean Southward

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