## Date of Award

12-1974

## Document Type

Dissertation - Restricted

## Degree Name

Doctor of Philosophy (PhD)

## Department

Chemistry

## First Advisor

David Schrader

## Second Advisor

Robert Brebrick

## Third Advisor

Paul Feng

## Fourth Advisor

Scott Kittsley

## Fifth Advisor

Smio Tani

## Abstract

This work is a quantum mechanical study of model potential theory for positron-atom systems, both bound and scattering. The difficulties of obtaining an accurate wave function to interpret the positron annihilation parameters by the variational approach, even for the simple e+H system, are mentioned. Existing model potentials and pseudopotentials are reviewed and none of them are found to be directly applicable to positronic systems. We propose a simple and theoretically based model potential method which is suitable to perform the calculations to a good accuracy.

Positronic systems are poorly understated experimentally. Therefore, in order to test our idea, we must do calculations on purely electronic systems. The potential arising from the polarization of the two core electrons by the valence electron in the lithium atom is derived by the perturbation theory in the adiabatic approximation. If the zeroth order core wave function is taken to be a product of single-zeta orbitals and if core-valence exchange is neglected, then the resulting. first order equation for the core orbitals is identical to that for the two-electron atomic system first considered by Bethe (Handbuch der Physik, 24/1, Springer-Verlag, Berlin, 1943, P; 324-349) and solved exactly in general form by Reeh (Z. Naturforsh. 15a., 377,1960). We calculate energies for a number of bound states of a valence electron moving in this polarized core potential, and compare our results to several widely used core polarization potentials. All of the potentials compared have been used and compared extensively in electron-atom scattering calculations, but this is the first comparison for a bound electron moving about a closed shell core.

If the zeroth order core function is a product of Hartree-Fock orbitals, then the first order equation for the core orbital is the same as that for electron-helium scattering {Phys. Rev. 147, 28, 1966). These authors expressed the core-valence interaction as a multipole expansion and solved only the=0, 1, 2 contributions to the first order equation. We solve the equation by the second order variational perturbation method, and are able to account for all multipole contributions in one equation. Then, the Hartree-Fock polarization potential is expressed in multipole form or for all multipole together by different choices of basis functions. This Hartree-Fock adiabatic polarization potential is compared to that obtained with single zeta core orbitals.

Non-adiabatic corrections appear in both the valence and perturbed core equations. Methods for calculating non-adiabatic effects by the second order perturbation method are discussed. A proposed model potential for a positron outside a core consists of a frozen core Coulomb potential plus a core polarization potential plus non-adiabatic corrections.

For a more complicated system, e.g. positronium-atom,

the model potential for the outside electron should include the exchange effect among electrons. An exchange core polarization potential is derived by the perturbation method. The perturbation is defined as the sum of the electrostatic effect and the exchange effect. This exchange core polarization theory is directly applicable to the systems with one outer electron plus two core electrons (for example, lithium bound states and electron-helium scattering systems).