Journal of Physics B: Atomic, Molecular and Optical Physics
The angular and radial components of electron correlation have each been examined in detail for the discrete 2p2 3P states of H-, He, Li+ and Be2+. These doubly excited systems were described by highly accurate explicitly correlated wavefunctions. The analysis involved the use of angular Coulomb holes, changes in the one- and two-particle radial density distributions and several angular and radial expectation values. Additionally, various statistical correlation coefficients were used which emphasized, in turn, angular and radial correlation properties in different regions of the two-particle density. The angular holes and related properties showed a clearly defined inverse-Z effect for He and the positive ions. This trend was not repeated for the radial curves. However, the radial densities did reveal a distinct 'in-out' correlation effect-similar in character to the split-shell behaviour for the ground state. By comparison with the findings for Z ≥ 2, the angular and radial correlation effects for H- were always exceedingly large, thus setting it apart from the other systems. For He, the angular hole for the comparatively slow moving 2p2 3P electrons was found to be over 50% deeper than that for the ground state and about six times the depth of a 1s2p 3P hole. The statistical correlation coefficients highlighted a steady growth, with Z, in the relative importance of angular correlation. Nevertheless, for each system, these coefficients indicated that the radial effect was the prevailing influence on the two-particle probability distribution.
Keeble, D. R. T.; Banyard, K. E.; and Drake, Gordon W. F.. (1993). Angular and radial correlation in doubly excited systems when 1 ≤ Z ≤ 4. The 2p2 3P state. Journal of Physics B: Atomic, Molecular and Optical Physics, 26 (17), 2811-2825.