Unitarity potentials and neutron matter at the unitary limit

TL;DR

This paper investigates the universal behavior of neutron matter at the unitary limit by calculating the energy ratio using various unitarity potentials, confirming its independence from interaction details and close to the expected universal value.

Contribution

The study introduces a method to compute the energy ratio in neutron matter at the unitary limit using different unitarity potentials, demonstrating its universality.

Findings

The energy ratio .44 is consistent across different unitarity potentials.

The ratio .44 remains close to the universal value regardless of interaction details.

A sum-rule and scaling constraint for low-momentum interactions is discussed.

Abstract

We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $\xi=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\xi\sim 0.44(1)$. In the present work we calculate this ratio $\xi$ using a family of hard-core square-well potentials whose $a_s$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite $a_s$. We have also calculated $\xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\xi$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is discussed.