Date of Award


Publication Type

Doctoral Thesis

Degree Name




First Advisor

Gordon Drake


Pure sciences, Asymptotic expansion, Helium-like ions, Rydberg electron




The aim of this work is to explore the range of validity of the asymptotic expansion method for a nuclear charge Z ≥ 3. The asymptotic expansion method provides a simple analytical method to calculate the energies and properties of atoms with one electron in a highly excited state called a Rydberg state. The method was originally developed by Drachman from an expansion of the optical potential [7,81 for the Rydberg electron in powers of the perturbing potential and later reformulated by Drake based on a simple perturbation expansion for the total wave function. The method takes advantage of the fact that, with increasing angular momentum, the overlap of the Rydberg electron wave function with the core consisting of a 18 electron and the nucleus becomes vanishingly small. For a helium atom (Z = 2) with an angular momentum L≥7, the asymptotic method can be used as a high precession computational method, but for Z ≥ 3 we have to increase the angular momentum to consider the asymptotic expansion as a high precession computational method as explained in chapter two. It provides a simple picture of the complex physics involved. This thesis extends the asymptotic expansion method to helium like ions for any value of Z and tests its accuracy against high precision variational calculations [311 for angular momentum L up to 7 and nuclear charge up to 18. For the exited states variational calculations become more difficult and the results' accuracy is inversely proportional with increasing angular momentum, in this case the asymptotic expansions take over variational calculations.