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

TL;DR

This paper derives normalization sum rules for electron pair densities in the homogeneous electron gas, linking two-body scattering phase shifts to the one-body momentum distribution via Overhauser geminals.

Contribution

It introduces new sum rules connecting pair density normalization to scattering phase shifts and the momentum distribution in the electron gas.

Findings

Sum rules relate pair densities to phase shifts.

Geminal parametrization successfully applied.

Links two-body and one-body properties.

Abstract

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.