### 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 |

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### Cite this

*Journal of Physics B: Atomic and Molecular Physics*,

*19*(11), 1595-1605. [014]. https://doi.org/10.1088/0022-3700/19/11/014

}

*Journal of Physics B: Atomic and Molecular Physics*, vol. 19, no. 11, 014, pp. 1595-1605. https://doi.org/10.1088/0022-3700/19/11/014

**A model wavefunction including electron correlation for the ground state of the helium isoelectronic sequence.** / Abbott, P. C.; Maslen, E. N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A model wavefunction including electron correlation for the ground state of the helium isoelectronic sequence

AU - Abbott, P. C.

AU - Maslen, E. N.

PY - 1986/12/1

Y1 - 1986/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0005625558&partnerID=8YFLogxK

U2 - 10.1088/0022-3700/19/11/014

DO - 10.1088/0022-3700/19/11/014

M3 - Article

VL - 19

SP - 1595

EP - 1605

JO - Journal of Physics B: Atomic and Molecular Physics

JF - Journal of Physics B: Atomic and Molecular Physics

SN - 0022-3700

IS - 11

M1 - 014

ER -