Boundary solutions of the two-electron Schrädinger equation at two-particle coalescences of the atomic systems

E. Z. Liverts*, M. Ya Amusia, R. Krivec, V. B. Mandelzweig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate correlation function hyperspherical harmonic method wave functions. The asymptotic solutions of the proper two-electron Schrödinger equation have been derived for both electron-nucleus and electron-electron coalescence. It is shown that the solutions for the electron-nucleus coalescence correspond to the ground and singly excited bound states, including triplet ones. The proper solutions at small distances R from the triple coalescence point were presented as the second order expansion on R and ln R. The vanishing of the Fock’s logarithmic terms at the electron-nucleus coalescence line was revealed in the frame of this expansion, unlike the case of electron-electron coalescence. On the basis of the obtained boundary solutions the approximate wave function corresponding to both coalescence lines have been proposed in the two-exponential form with no variational parameters.

Original languageEnglish
Article number012514
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume73
Issue number1
DOIs
StatePublished - 2006

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