Pairing of the P\"oschl-Teller gas

TL;DR

This paper investigates the equation of state and pairing properties of a cold Fermi gas with P"oschl-Teller interactions, revealing an instability at low density and significant effects of non-local correlations on the pairing gap.

Contribution

It provides new calculations of the equation of state and pairing gap for a P"oschl-Teller interacting Fermi gas, highlighting the role of correlations and non-localities.

Findings

Gas exhibits low-density instability indicated by divergence of in-medium scattering length.

Non-local correlations can alter the pairing gap by nearly an order of magnitude.

Instability occurs before the divergence of vacuum scattering length.

Abstract

We report calculations of equation of state of a model system, representative for a cold Fermi gas, of particles interacting via the P\"oschl-Teller interaction. In successively more sophisticated calculations, we determine the importance of correlations and non-localities. We show that the gas displays, at relatively low density, an instability indicated by a divergence of the in-medium scattering length which occurs well before the divergence of the vacuum scattering length and the spinodal density. We also calculate the pairing gap and show that non-local correlations can change the pairing gap by almost an order of magnitude.