Date of Award


Degree Type


Degree Name




First Advisor

Drake, Gordon


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


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).