Spin 1/2 Fermions in the Unitary Limit.II

TL;DR

This paper investigates the energy of spin 1/2 fermions in the unitary limit, showing the significant impact of effective range on energy calculations and emphasizing the importance of verifying unitarity in interactions.

Contribution

It extends previous work by including finite effective range effects and analyzing their influence on the energy in the unitary limit.

Findings

Energy increases with effective range, reaching ~0.4 for r_0=1 fm.

Interaction resonance observed near the unitary limit.

Energy estimates vary significantly depending on interaction parameters.

Abstract

This report concerns the energy of a zero-temperature many-body system of spin 1/2 fermions in the unitary limit. In a previous report (arXiv:0705.0944) this energy was determined to be xi~0.24 in units of the free gas kinetic energy, appreciably lower than most reports giving ~0.45$. In our calculation the 2-body interaction satisfied exactly the unitary limit i.e. infinite scattering length and effective range r_0=0. In the present report results with r_0>0are shown. A strong dependence on the effective range is found. It is for example found that an increase to r_0=1 fm increases xi to ~ 0.4 close to other reports of xi in the unitary limit. It is concluded that because of the singular character of the unitary limit it is necessary to verify that the interaction actually satisfies unitarity. The calculations done here in a pp-ladder approximation show a resonance in the in-medium interaction close to (and in) the unitary limit. This was already found in the previous work.