Correlated Pair Approach to Composite Boson Scattering Lengths

TL;DR

This paper develops a new theoretical approach to calculate the scattering lengths of composite bosons using correlated-pair states, revealing the role of fermion exchange and providing models that match numerical results.

Contribution

It introduces a correlated-pair basis method for coboson scattering, improving understanding and modeling of fermion exchange effects in composite boson interactions.

Findings

Scattering lengths for different potentials are calculated, with some matching Born values and others being smaller.

Results for fermionic-atom dimers and excitons agree with more demanding numerical methods.

Separable model scatterings are proposed that match numerical results across mass ratios.

Abstract

We derive the scattering length of composite bosons (cobosons) within the framework of the composite boson many-body formalism that uses correlated-pair states as a basis, instead of free fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the s-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable, and that produce scattering lengths which match quantitatively well with the numerically-obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.