A model wavefunction including electron correlation for the ground state of the helium isoelectronic sequence

P. C. Abbott, E. N. Maslen

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

From the form of the exact ground-state wavefunction psi , of a helium-like atom, the dependence on the first power of the interparticle coordinates r 1, r2 and r12 is easily obtained. The authors construct a simple model wavefunction phi that (a) agrees with the exact wavefunction to first order in r1, r2 and r12, (b) is finite everywhere, is normalisable and satisfies the derivative cusp conditions as r1, r2 or r12 to 0, and (c) satisfies the virial theorem. If the exact wavefunction psi is written psi = phi chi , then chi satisfies a transformed Schrodinger equation, H' chi =E chi where H' has no poles at the electron-nucleus or electron-electron coalescences. It is shown, by a linear transformation of the interparticle coordinates, that all integrals required for the evaluation of the energy reduce to products of gamma functions.

Original languageEnglish
Article number014
Pages (from-to)1595-1605
Number of pages11
JournalJournal of Physics B: Atomic and Molecular Physics
Volume19
Issue number11
DOIs
Publication statusPublished - 1 Dec 1986

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isoelectronic sequence
helium
ground state
gamma function
linear transformations
virial theorem
electrons
helium atoms
cusps
coalescing
poles
nuclei
evaluation
products
energy

Cite this

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abstract = "From the form of the exact ground-state wavefunction psi , of a helium-like atom, the dependence on the first power of the interparticle coordinates r 1, r2 and r12 is easily obtained. The authors construct a simple model wavefunction phi that (a) agrees with the exact wavefunction to first order in r1, r2 and r12, (b) is finite everywhere, is normalisable and satisfies the derivative cusp conditions as r1, r2 or r12 to 0, and (c) satisfies the virial theorem. If the exact wavefunction psi is written psi = phi chi , then chi satisfies a transformed Schrodinger equation, H' chi =E chi where H' has no poles at the electron-nucleus or electron-electron coalescences. It is shown, by a linear transformation of the interparticle coordinates, that all integrals required for the evaluation of the energy reduce to products of gamma functions.",
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A model wavefunction including electron correlation for the ground state of the helium isoelectronic sequence. / Abbott, P. C.; Maslen, E. N.

In: Journal of Physics B: Atomic and Molecular Physics, Vol. 19, No. 11, 014, 01.12.1986, p. 1595-1605.

Research output: Contribution to journalArticle

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