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arXiv · 2602.17420

Hartree shift and pairing gap in ultracold Fermi gases in the framework of low-momentum interactions

Michael Urban·S. Ramanan
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Abstract

In this paper we consider a two-component gas of fermions on the BCS side of the BCS-BEC crossover at zero temperature. We use a momentum dependent interaction that reproduces the s-wave scattering phase shifts of a contact interaction up to a momentum cutoff that is scaled with the Fermi momentum. Using a diagrammatic formulation of Bogoliubov many-body perturbation theory, suitably augmented by self-consistency conditions, we obtain the Hartree shift and the pairing gap to third order. In the weak-coupling regime, our results are not only well-converged but also agree with the well-established Gor'kov-Melik-Barkhudarov corrections for the gap and the Galitskii result for the Hartree shift. Near the unitary regime, our results for the Nambu-Gor'kov self-energy are less converged, but there is still reasonable agreement with experiments as well as with quantum Monte-Carlo results. Perspectives for improvements and applications of this approach to neutron matter are discussed.

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Michael Urban, S. Ramanan. 2026-02-19. Hartree shift and pairing gap in ultracold Fermi gases in the framework of low-momentum interactions. https://doi.org/10.1103/w6mp-38jz

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