Hylleraas-like functions with correct cusp conditions: critical charge

J. M. RANDAZZO, V. Y. GONZÁLEZ, A. L. FRAPICCINI, F. D. COLAVECCHIA AND G. GASANEO

Santos, Brasil

Conferencia; 18th International IUPAP Conference on Few-Body Problems in Physics; 2006

In this report we present a method that provides an approximate solution of the Schrodinger equation of the three-body problem. It is based on the pseudo-separable method, originally proposed by Pluvinage. Hylleraas-like wavefunctions are constructed for the He atom and its isoelectronic sequence, in terms of exponential and power serieIn this work we present the results obtained by minimizing the mean energy of the ground state of the He atom and its isoelectronic sequence. We study functions having up to 14 parameters. The accuracy of the calculated energies is found to be about 10^{-4} a.u.. We also evaluate mean values of several physical quantities, and study the behaviour of the two-electron systems near the critical nuclear charge. Among the different ions in the isoelectronic sequence, we study, in particular, the H^{-} ion. It is an important prototype system for the study of correlations because the electron-electron repulsion is equal, in strength, to the electron-nucleus attraction. As a consequence, the two electrons are loosely bound in the ground state of H^{-}, being very sensitive to correlation effects.