Low-momentum ring diagrams of neutron matter at and near the unitary limit

TL;DR

This paper investigates neutron matter near the unitary limit using low-momentum ring diagrams, revealing a universal energy ratio close to 0.44, consistent with experimental and Monte Carlo results.

Contribution

It introduces a method to compute neutron matter energy near the unitary limit using low-momentum ring diagrams and demonstrates universality in the energy ratio across various scattering lengths.

Findings

The energy ratio approaches 0.44 at the unitary limit.

The results are consistent with experimental and Monte Carlo studies.

Comparison of ring-diagram results with G-matrix interactions.

Abstract

We study neutron matter at and near the unitary limit using a low-momentum ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential, neutron-neutron potentials with various $^1S_0$ scattering lengths such as $a_s=-12070fm$ and $+21fm$ are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding $a_s$-equivalent low-momentum potentials $V_{low-k}$, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy $E_0$ of neutron matter for various scattering lengths. At the limit of $a_s\to \pm \infty$, our calculated ratio of $E_0$ to that of the non-interacting case is found remarkably close to a constant of 0.44 over a wide range of Fermi-momenta. This result reveals an universality that is well consistent with the recent experimental and Monte-Carlo computational study on low-density cold Fermi gas at the unitary limit. The overall behavior of this ratio obtained with various scattering lengths is presented and discussed. Ring-diagram results obtained with $V_{low-k}$ and those with $G$-matrix interactions are compared.