A new effective interaction for the trapped fermi gas: the BEC-BCS crossover

TL;DR

This paper introduces an improved effective interaction for trapped Fermi gases that accelerates convergence in few-body calculations across the BEC-BCS crossover, enhancing computational efficiency and accuracy.

Contribution

The authors extend a separable interaction to all scattering lengths and analytically demonstrate its convergence properties, improving upon traditional contact interactions.

Findings

Faster convergence of low-lying energies with the new interaction.

Analytical expressions for interaction matrix elements and eigenvectors.

Enhanced accuracy in three- and four-particle systems across the crossover.

Abstract

We extend a recently introduced separable interaction for the unitary trapped Fermi gas to all values of the scattering length. We derive closed expressions for the interaction matrix elements and the two-particle eigenvectors and analytically demonstrate the convergence of this interaction to the zero-range two-body pseudopotential for s-wave scattering. We apply this effective interaction to the three- and four-particle systems along the BEC-BCS crossover, and find that their low-lying energies exhibit convergence in the regularization parameter that is much faster than for the conventional renormalized contact interaction. We find similar convergence properties of the three-particle free energy at unitarity.