Physics & Astronomy ETDs

Publication Date

5-1-1968

Abstract

A computational investigation of the effect of a surface transition region of relative half-width δ on certain surface resonances in high frequencies scattering from a nearly-sharp, three dimensional spherical well is performed by the method of partial wave analysis.

An incident beam of particles, described by a scalar plane wave, interacts with a fixed scattering center represented by a dielectric sphere of index of refraction 1.333, with a very small transition region in the boundary of the well, described by an odd polynomial function of third order. This is the scalar-wave analogue to the more complicated problem of scattering of light from water droplets.

For the case of size parameter (propagation constant times the well radius) near 200, four different resonances were found, each of which has a period of about 0.81 in the size parameter X.

Plots of the size parameter at the resonances and the average probability density of finding the particle inside the well (excluding the transition zone) vs the half-width of the transition region, δ, were made and a linear dependence in each case was found for small values of δ. Also, a plot of the width of the resonances (which are assumed to have a Lorentzian line shape behavior) vs δ was made and is shown to be related to the graph of the probability density vs δ.

The calculations demonstrate that the surface resonance excited by a monochromatic beam of particles in the resonance regions is due mainly to the terms in the partial wave expansion representing the highest contributing value of the angular momentum.

Degree Name

Physics

Level of Degree

Masters

Department Name

Physics & Astronomy

First Committee Member (Chair)

Christopher Pratt Leavitt

Second Committee Member

Seymour Samuel Alpert

Third Committee Member

Derek B. Swinson

Language

English

Document Type

Thesis

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