LSU Historical Dissertations and Theses

1990

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics and Astronomy

A. R. P. Rau

Abstract

In this dissertation on the structure and properties of doubly excited state of atoms, we are interested in states of atoms where two electrons are highly and comparably excited. Such states have been named doubly excited ridge states. Angular and radial correlations of two electrons in such states are of interest. First a semi-empirical study, based on available data, is carried out to test the validity of a pair quantum number descriptions in which a single six-dimensional Rydberg formula is proposed to organize sequences of doubly excited states as a function of energy. Next, we make a detailed analysis of angular correlations to see their origins. Models in which the principal quantum numbers n are held fixed already account for the dominant features and consequences of angular correlations, but the coupling of states from different n which are included in one particular study, called the Wannier theory, are also significant. In the final chapter, an analytical study of ridge states is presented by using a wave function that treats the pair of electrons as a single entity in solving the two electron Schrodinger equation. Pair "hyperspherical" coordinates R = $\sqrt{\rm r\sb1\sp2 + r\sb2\sp2}$, $\alpha$ = arctan $\rm ({r\sb2\over r\sb1})$ and $\theta\sb{12}$ = arccos $\rm (\ r\sb2 \cdot \ r\sb1)$ are used. Borrowing from the Wannier theory for the similar situation of two comparable slow electrons in the continuum and the radial ($\alpha$) and angular $(\theta\sb{12})$ correlations between them, the dominant part of the wave function for ridge states may be expected to lie in the region $\rm \vec r \sb1 = -\vec r \sb2$, that is, $\alpha$ = $\pi\over 4$ and $\theta\sb{12}$ = $\pi$. By expanding the Schrodinger equation around these points and retaining the first non-trivial quadratic dependences in $\alpha$ and $\theta\sb{12}$, we seek a solution in which the form of the wave function in these two variables is analytically determined as in the Wannier theory. The dependence on R is then handled numerically and with a structure appropriate for bound states, numerical eigenvalues for ridge states are calculated and compared with other available results. These results do bear out a pair of Rydberg formulae for organizing sequences of ridge states, thereby providing a theoretical justification for the pair description.

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