Date of Award


Publication Type

Master Thesis

Degree Name





Pure sciences, Critical nuclear charge, Hylleraas, Puiseux, Variational method


Drake, Gordon W. F.




For an atom there exists a critical nuclear charge Z c that is just sufficient to bind the nucleus and its electrons into a stable configuration. A study of the critical charge for two-electron atoms is presented with the purpose of improving accuracy for Z c . To this end, high precision techniques involving the variational method with multiple basis sets in Hylleraas coordinates are employed. The method is particularly well adapted to the case where one electron is strongly bound and the other is at the limit of becoming unbound. The results are analysed in terms of fractional powers of ( Z - Z c ) related to the analytic structure of the energy E ( Z ) and a 1/ Z expansion for the energy. This results in a Z c of 0.91102808(5). Future work prompted by this study includes development of direct techniques to determine Z c utilizing the low-Z stability of the method; developing the framework and mathematical justification for a novel bootstrap analysis method used in curve-fitting; and investigating the inclusion of finite nuclear mass, relativistic effects, and other higher order corrections in the determination of Z c .