Doctoral Dissertations

Keywords and Phrases

atom surface interaction; calcium fluoride; Casimir forces; dielectric function; retardation; silicon

Abstract

In this dissertation, we propose a uniform functional form of the dielectric function of solids that is applicable over a wide range of frequencies. We apply our model to describe the dielectric function of two technologically important materials: silicon and calcium fluoride. The temperature dependence of their dielectric functions is also described using simple analytic forms. We found that a generalized Sellmeier-type model with complex denominators (“damped oscillators”) does not lead to a satisfactory fit of experimental data for the dielectric function. In contrast, our model, which is analytically only slightly more involved (“complex oscillator strengths”, complex numerators), allows us to model the dielectric function of the materials from the infrared (IR) to the ultraviolet (UV) region, with excellent statistics. This functional form naturally arises when the dielectric function is composed as a retarded Green function of damped coupled oscillators, which also takes the radiation reaction into account. Thus, the model is referred to as the radiation–reaction improved coupled–oscillator (RRCO) model. Atom–surface interactions of several atomic species, including ground-state hydrogen, ground-state helium, and metastable (23S1) helium have been studied for silicon and calcium fluoride surfaces. These profit from improved simplified calculational methods for the dynamic polarizability of the interacting atoms. In our investigation, we have found that the transition from the nonretarded van der Waals regime to the retarded Casimir–Polder regime is primarily characterized by the largest characteristic frequency in the system, which comes from the atom, not the surface. Our simple estimate for the critical distance, Zcr (onset of retardation), is given in atomic units as Zcr = 137 √︁(∞(0)/Z), where ∞(0) is the static polarizability of the interacting atom, Z is its number of electrons, and Zcr is measured in Bohr radii. Our work paves the way for an improved understanding of atom–surface interactions, concerning both the dielectric function that enters the description of the optical surface properties, as well as the atomic dynamic polarizability, for which we find a simplified, streamlined analytic approach.

Advisor(s)

Jentschura, Ulrich D., 1969-

Committee Member(s)

Yamilov, Alexey
Ullrich, Carsten A.
Schulz, Michael, 1959-
Vojta, Thomas

Department(s)

Physics

Degree Name

Ph. D. in Physics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2026

Pagination

x, 154 pages

Note about bibliography

Includes_bibliographical_references_(pages 146-153)

Rights

© 2026 Tuhin Kanti Das , All Rights Reserved

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 12589

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Physics Commons

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