The Electron-Gas Pair Densities and their Normalization Sum Rules in Terms of Overhauser Geminals and Corresponding Scattering Phase Shifts

It is shown, how the normalization sum rules of the spin-parallel and spin-antiparallel pair densities of the homogeneous electron gas become sum rules for the scattering phase shifts of the Overhauser two-body wave functions (geminals), with which the pair densities have been successfully parametrized recently. These new sum rules relate two-body quantities to a one-body quantity, namely the asymptotics of the Overhauser geminals to the momentum distribution.