  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.
