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The aim of this work is to apply trial functions constructed from Hylleraas functions with three independent sets of nonlinear scale factors to variational calculations for helium and helium-like ions. The ground state and low-lying Rydberg energy levels of these ions have been calculated to several orders of magnitude greater accuracy than previous work in this area while using an equal, or in most cases, a reduced number of basis functions. Each of the three sectors of the basis set is found to describe a different scale of coordinate space corresponding to the asymptotic, intermediate, and close-ranged distances between particles. The incorporation of the third, close-ranged sector, allows the basis set to better model complex correlation effects between the nucleus and the two electrons in the atomic three-body problem. Optimization of the basis set parameters is achieved through standard variational techniques and the validity of the wave functions near the electron-nucleus and electron-electron coalescence points is tested using the Kato cusp conditions. The tripled basis set is also applied to the 1/ Z perturbation expansion as a case study. A multiple-precision package, MPFUN90 written by David H. Bailey, was used to alleviate numerical instabilities which arose for certain states.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .N57. Source: Masters Abstracts International, Volume: 43-01, page: 0225. Adviser: G. W. F. Drake. Thesis (M.Sc.)--University of Windsor (Canada), 2004.
Nistor, R. A., "Improved strategies for variational calculations for helium" (2004). Electronic Theses and Dissertations. 2402.