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

C. N. Gilbreth; Y. Alhassid

doi:10.1103/physreva.85.033621

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arXiv · 1108.2687

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

C. N. Gilbreth·Y. Alhassid

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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.

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C. N. Gilbreth, Y. Alhassid. 2011-08-12. A new effective interaction for the trapped fermi gas: the BEC-BCS crossover. https://doi.org/10.1103/physreva.85.033621

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