Equation of state of superfluid neutron matter with low-momentum interactions

TL;DR

This paper calculates the ground state energy of pure neutron matter using low-momentum interactions within a perturbative framework, emphasizing the importance of pairing and cutoff dependence at low densities relevant to neutron star crusts.

Contribution

It introduces a density-dependent cutoff in $V_{low-k}$ interactions and applies third-order perturbation theory around the HFB state, improving the understanding of neutron matter at low densities.

Findings

Including pairing improves perturbation convergence at low densities.

Higher-order corrections reduce cutoff dependence.

The method is relevant for neutron star crust modeling.

Abstract

In this work, we calculate the ground state energy of pure neutron matter using the renormalization group based low-momentum effective interaction $V_{\text{low-}k}$ in Bogoliubov many-body perturbation theory (BMBPT), which is a perturbative expansion around the Hartree-Fock-Bogoliubov (HFB) ground state. In order to capture the low-density behavior of neutron matter, it turns out to be better to use a density dependent cutoff in the $V_{\text{low-}k}$ interaction. Perturbative corrections to the HFB energy up to third order are included. We find that at low densities corresponding to the inner crust of neutron stars, the HFB state that includes pairing is a better starting point for perturbation expansion. It is observed that including the higher order perturbative corrections, the cutoff dependence of the ground state energy is reduced.