The electron-gas pair density and its geminal representation - II. The long-range asymptotics of the Kimball-Overhauser geminals

摘要

In part I [phys. stat. sol. (b) 241, 3544 (2004)] it has been shown, for the homogeneous electron gas, how the momentum distribution n(k) determines the geminal occupancy mu(k), which appears in the KimballOverhauser partial-wave analysis of the pair density g(r). The Fermi surface singularities of n(k) cause singularities in p(k). These singularities determine the large-r asymptotics of the 1 -matrix and of the pair density, respectively. Because the pair-density geminals are scattering states, their asymptotic behavior is characterized by phase shifts. Whereas the normalization sum rule of g(r) leads to a Friedel-like phaseshift sum rule [Phys. Rev. B 67, 233102 (2003)], the plasmon sum rule cannot be satisfied by KimballOverhauser geminals. Possibilities to cure this failure are discussed.