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An Expansion Method for Calculating Atomic Properties. VIII. Transitions in the Hartree-Fock Approximation

M. Cohen and A. Dalgarno
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 293, No. 1434 (Aug. 9, 1966), pp. 359-364
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/2415474
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
An Expansion Method for Calculating Atomic Properties. VIII. Transitions in the Hartree-Fock Approximation
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Abstract

According to Brillouin's theorem, diagonal matrix elements of one-electron operators are given correct to first order by the Hartree-Fock approximation. Transition matrix elements of one-electron operators are not given correct to first order because of the contributions from virtual excitations involving a change in the azimuthal quantum number of the active electron but no change in the principal quantum number. The electric dipole matrix elements connecting the 1s2s$^{1,3}$S states of helium to the 1s2p$^{1,3}$P states are calculated exactly to first order in inverse powers of the nuclear charge and the differences from the Hartree-Fock approximation are shown explicitly to correspond to virtual transitions of the inner shell 1s electron of the type 1s-np. A generalization of the Hartree-Fock approximation is discussed which eliminates most of the first order error.

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