dorsal/arxiv
View SchemaBoundary Solutions of the Two-electron Schrodinger Equation at Two-particle Coalescences of the Atomic Systems
| Authors | E. Z. Liverts, M. Ya. Amusia, R. Krivec, V. B. Mandelzweig |
|---|---|
| Categories | |
| ArXiv ID | physics/0510247 |
| URL | https://arxiv.org/abs/physics/0510247 |
| DOI | 10.1103/PhysRevA.73.012514 |
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 CFHHM wave functions. The asymptotic solutions of the proper two-electron Schrodinger 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 lnR. 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.
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"abstract": "The limit relations for the partial derivatives of the two-electron atomic\nwave functions at the two-particle coalescence lines have been obtained\nnumerically using accurate CFHHM wave functions. The asymptotic solutions of\nthe proper two-electron Schrodinger equation have been derived for both\nelectron-nucleus and electron-electron coalescence. It is shown that the\nsolutions for the electron-nucleus coalescence correspond to the ground and\nsingly excited bound states, including triplet ones. The proper solutions at\nsmall distances $R$ from the triple coalescence point were presented as the\nsecond order expansion on R and lnR. The vanishing of the Fock\u0027s logarithmic\nterms at the electron-nucleus coalescence line was revealed in the frame of\nthis expansion, unlike the case of electron-electron coalescence. On the basis\nof the obtained boundary solutions the approximate wave function corresponding\nto both coalescence lines have been proposed in the two-exponential form with\nno variational parameters.",
"arxiv_id": "physics/0510247",
"authors": [
"E. Z. Liverts",
"M. Ya. Amusia",
"R. Krivec",
"V. B. Mandelzweig"
],
"categories": [
"physics.atom-ph",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevA.73.012514",
"title": "Boundary Solutions of the Two-electron Schrodinger Equation at Two-particle Coalescences of the Atomic Systems",
"url": "https://arxiv.org/abs/physics/0510247"
},
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