Neutron matter at low density and the unitary limit

TL;DR

This study investigates low-density neutron matter using the hole-line expansion, revealing that the equation of state is mainly influenced by the $^1S_0$ channel, with results close to the unitary limit and minimal three-body force effects.

Contribution

It provides a detailed analysis of neutron matter at low densities, showing that simplified models closely match full calculations and that the equation of state remains well-behaved below $k_F=0.4$ fm$^{-1}$.

Findings

Equation of state dominated by $^1S_0$ channel.

Three-body forces contribute minimally.

Results remain stable below $k_F=0.4$ fm$^{-1}$.

Abstract

Neutron matter at low density is studied within the hole-line expansion. Calculations are performed in the range of Fermi momentum $k_F$ between 0.4 and 0.8 fm$^{-1}$. It is found that the Equation of State is determined by the $^1S_0$ channel only, the three-body forces contribution is quite small, the effect of the single particle potential is negligible and the three hole-line contribution is below 5% of the total energy and indeed vanishing small at the lowest densities. Despite the unitary limit is actually never reached, the total energy stays very close to one half of the free gas value throughout the considered density range. A rank one separable representation of the bare NN interaction, which reproduces the physical scattering length and effective range, gives results almost indistinguishable from the full Brueckner G-matrix calculations with a realistic force. The extension of the calculations below $k_F = 0.4$ fm$^{-1}$ does not indicate any pathological behavior of the neutron Equation of State.