Coulomb correlation in a doubly occupied K shell: the influence of outer electrons

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Abstract
K-shell electron correlation effects within Li+(1S), Li(2S), Li(2P), Li-(1S), Be2+(1S) Be+(2S), Be+(2P) and Be(1S) are examined in position and momentum space. The assessment is made in terms of Coulomb 'holes' Delta f(r12) and 'shifts' Delta f(p12), partial Coulomb 'holes' Delta g(r12;r1) and 'shifts' Delta g(p12;p1), and the correlation-induced changes in various statistical correlation coefficients, Delta tau . For each space, tau are chosen which reflect the angular and radial components of correlation in different regions of the doubly occupied K shell. From such an overview, the changes in the K alpha K beta correlation effects arising from the interaction of an outer electron could be ascertained and rationalised. In position space, the K-shell results for Delta f(r12) and Delta g(r12;r1) were only marginally affected. Nevertheless, the Delta tau values did suggest changes of emphasis between the angular and radial correlation components. For the complementary momentum space, however, Delta f(p12), Delta g(p12;p1) and the Delta tau values were found to be quite sensitive to the occupation and nature of the outer orbital, whether 2s or 2p. The momentum results were, therefore, the most informative. Besides highlighting the influence of occupied outer orbitals on the correlation effects within a doubly occupied inner shell, the present study demonstrates, very forcefully, the necessity for such examinations to be carried out in momentum space.