Many-Body Perturbation Theory Applied to Atoms

Many-body perturbation theory as formulated by Brueckner and Goldstone is applied to atoms to obtain corrections to Hartree-Fock wave functions and energies. Calculations are made using a complete set of single-particle Hartree-Fock wave functions which includes both the continuum and an infinite number of bound states. It is shown how one may readily perform the sums over an infinite number of bound excited states. In order to demonstrate the usefulness of many-body perturbation theory in atomic problems, calculations are made for a wide variety of properties of the neutral beryllium atom. The calculated $2s\ensuremath{-}2s$ correlation energy is -0.0436 atomic unit for $l=1$ excitations. The calculated dipole and quadrupole polarizabilities are 6.93\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$ and 14.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}40}$ ${\mathrm{cm}}^{5}$, respectively. The calculated dipole and quadrupole shielding factors are 0.972 and 0.75. Results are given for oscillator strengths, photoionization cross sections, and the Thomas-Reiche-Kuhn sum rule, which is 4.14 as compared with 4.00, the theoretical value.

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