Pairing of the P\"oschl-Teller gas

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.