Analytic matrix elements for the two-electron atomic basis with logarithmic terms

Evgeny Z. Liverts, Nir Barnea

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Abstract

The two-electron problem for the helium-like atoms in S-state is considered. The basis containing the integer powers of ln?r, where r is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only elementary and special functions, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vicinity of the triple-coalescence point is reaffirmed.

Original languageAmerican English
Article number082104
JournalJournal of Mathematical Physics
Volume55
Issue number8
DOIs
StatePublished - 25 Jul 2014

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