First-Order Perturbation Corrections to the Hartree-Fock Approximation for Helium

A. W. Weiss and J. B. Martin

Phys. Rev. 132, 2118 – Published 1 December 1963

ABSTRACT

Variational perturbation theory has been used to compute the first-order wave function for the ground state of the helium atom, in a scheme where the Hartree-Fock function is treated as the zeroth-order approximation. The first-order function was approximated by a Hylleraas-like expansion, explicitly containing $r_{12}$. We obtain a total energy through third order of -2.90262 a.u., as compared with the nonrelativistic eigen-value of -2.90372. The first-order corrections to expectation values of a selection of one- and two-electron operators have been computed. The calculations have also been done for the isoelectronic ions, $H^{-}$, ${\mathrm{Li}}^{+}$, and ${\mathrm{Be}}^{2+}$.

• Received 18 July 1963

DOI:https://doi.org/10.1103/PhysRev.132.2118

©1963 American Physical Society

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