## Date of Award

6-2021

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Department of Mathematics and Statistics

## First Advisor

Mark Oxley, PhD

## Abstract

The Correlated Positronic-Electronic Orbital (CPEO) method was developed and implemented to capture correlation effects at between the positron and electron in the modeling of systems that involve a bound positron. Methods that effectively model these systems require many hundred basis functions and use a mean field approach as the beginning step. CPEO builds an orbital for virtual Positronium (Ps) that contains a positron in a bound state along with an accompanying electron to the larger system. Assigning the virtual Ps orbital allows for the two particle variational optimization in conjunction with the other particles that compose the whole system. This novel method required the mathematical development of Fock-operators for each of the three distinct Atomic Orbitals (AO) used in the model. Thus, the CPEO method required the solution of these three coupled Fock-operators. This approach results in the successful capture of positron-electron Coulomb correlation in a mean field method.

## AFIT Designator

AFIT-ENC-DS-21-J-001

## DTIC Accession Number

AD1144032

## Recommended Citation

Blaine, Kevin E., "Correlated Positron-electron Orbital (CPEO): A Novel Method that Models Positron-Electron Correlation in Virtual Ps at the Mean-Field Level" (2021). *Theses and Dissertations*. 5055.

https://scholar.afit.edu/etd/5055

## Comments

Alternate title form:Correlated Positron-electron Orbital (CPEO): A Novel Method that Models Positron-Electron Correlation in Virtual Positronium at the Mean-Field Level