Abstract
A theory for the coupling constants between spin-polarized degenerate fermionic atoms isdeveloped for the case of atoms confined to a quasi-one-dimensional harmonic trap.Exploiting the presence of the Fermi edge and the large number of fermions, it is shownthat the resulting effective one-dimensional interaction can be parametrized by three sets ofinteraction coefficients, two for forward scattering and one for backward scattering. In thecase of identical fermions, backscattering dominates, because the contact part of theeffective one-dimensional interaction must be subtracted. Analytic expressions forthe interaction coefficients for the effective contact interaction, which is relevantfor the inter-component interactions, and for the ‘p-wave’ interaction appearingin next order, are given. As an example, we calculate and discuss in detail theeffective coupling constants for the marginally long ranged dipole–dipole interaction.
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