New sum rules relating the 1-body momentum distribution of the homogeneous electron gas to the Overhauser 2-body wave functions of its pair density

TL;DR

This paper generalizes sum rules linking the 1-body momentum distribution of the homogeneous electron gas to Overhauser 2-body wave functions, enabling potential calculation of momentum distribution from phase shifts and effective interactions.

Contribution

It introduces generalized integral equations connecting pair density, phase shifts, and momentum distribution using Overhauser geminals and effective potentials.

Findings

Sum rules for scattering phase shifts are extended.

Integral equations for momentum distribution are formulated.

Potential to compute momentum distribution from phase shifts is demonstrated.

Abstract

The recently derived sum rules for the scattering phase shifts of the Overhauser geminals (being 2-body-wave functions which parametrize the pair density together with an appropriately chosen occupancy) are generalized to integral equations which allow in principle to calculate the momentum distribution, supposed the phase sifts of the Overhauser geminals are known from an effective parity-dependent interaction potential (screened Coulomb repulsion).