Correlated Pair Approach to Composite Boson Scattering Lengths

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.

arXiv comment10 pages, 6 figures

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Cited by in corpus (8)

• Entanglement between two spatially separated ultracold interacting Fermi gases
• Fermionic versus bosonic behavior of confined Wigner molecules
• On the description of composite bosons in discrete models
• Composite boson signature in the interference pattern of atomic dimer condensates
• Scattering amplitudes for dark and bright excitons
• Conserved operators and exact conditions for pair condensation
• Coboson many-body formalism for atom-dimer scattering length
• Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems