#### Date of Award

10-5-2017

#### Degree Type

Thesis

#### Degree Name

M.Sc.

#### Department

Physics

#### First Advisor

Drake, Gordon

#### Keywords

atomic physics, helium, perturbation theory, two-electron atoms

#### Rights

#### Abstract

This thesis solves a controversial physics problem that has existed in the literature for nearly a century { nding the radius of convergence of the perturbation expansion for the ground state energy of the two-electron atom. This problem is important to study because it makes progress towards nding the possible structures that can exist in the quantum mechanical three-body problem. This perturbation expansion is a convergent series and in physics these are rare to work with. We usually refer to this perturbation expansion as the \1=Z expansion". There is still much to learn about nding e ective methods of determining the radii of convergence for convergent series. The rst 1000 coe cients of the 1=Z expansion are calculated with very high precision and are compared to previous values in the literature. These coe cients are determined by using a new type of basis set that is introduced in this work, the pyramidal basis set, which is very useful in describing high-order wave functions generated by perturbation theory. Using the series of ratios of the resulting coe cients along with a series acceleration technique, the radius of convergence of the 1=Z expansion is found to be = 1:0975(2).

#### Recommended Citation

Peck, Ryan Louis, "Analysis of the Radius of Convergence of the Perturbation Expansion for the Ground State Energy of Two-Electron Atoms" (2017). *Electronic Theses and Dissertations*. 7289.

https://scholar.uwindsor.ca/etd/7289