## 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}, r_{2} and r_{12} is easily obtained. The authors construct a simple model wavefunction phi that (a) agrees with the exact wavefunction to first order in r_{1}, r_{2} and r_{12}, (b) is finite everywhere, is normalisable and satisfies the derivative cusp conditions as r_{1}, r_{2} or r_{12} 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 language | English |
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Article number | 014 |

Pages (from-to) | 1595-1605 |

Number of pages | 11 |

Journal | Journal of Physics B: Atomic and Molecular Physics |

Volume | 19 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Dec 1986 |