Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation

TL;DR

This paper investigates the momentum distribution of a three-dimensional Coulomb-interacting Fermi gas, showing it aligns with the random phase approximation and providing precise error bounds for relevant potentials.

Contribution

It refines previous analyses by establishing optimal error bounds for the momentum distribution near the Fermi surface in Coulomb systems.

Findings

Momentum distribution matches RPA predictions.

Provides optimal error bounds for Coulomb potentials.

Refines previous theoretical analysis with improved accuracy.

Abstract

We analyse the momentum distribution of a three-dimensional Fermi gas in the mean-field scaling regime in a trial state that was recently proven to reproduce the Gell-Mann-Brueckner correlation energy for Coulomb potentials. For a class of potentials including the Coulomb potential we show that the momentum distribution is given by a step profile corrected by a random phase approximation contribution as predicted by Daniel and Vosko. Moreover, for potentials with summable Fourier transform we provide optimal error bounds for the deviation from the random phase approximation. This refines a recent analysis by two of the authors to the physically most relevant potentials and to momenta closer to the Fermi surface.