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arXiv · 2511.03654

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

Niels Benedikter·Sascha Lill·Diwakar Naidu
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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. 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. The proof relies on a double bootstrap method, improved over the earlier analysis to estimate the momentum distribution both globally over all momenta and pointwise. We argue that a similar result can be expected to hold also for the ground state.

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Niels Benedikter, Sascha Lill, Diwakar Naidu. 2025-11-05. Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation. https://arxiv.org/abs/2511.03654

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