Atom-dimer scattering length for fermions with different masses: analytical study of limiting cases

Abstract

We consider the problem of obtaining the scattering length for a fermion colliding with a dimer, formed from a fermion identical to the incident one and another different fermion. This is done in the universal regime where the range of interactions is short enough so that the scattering length $a$ for non identical fermions is the only relevant quantity. This is the generalization to fermions with different masses of the problem solved long ago by Skorniakov and Ter-Martirosian for particles with equal masses. We solve this problem analytically in the two limiting cases where the mass of the solitary fermion is very large or very small compared to the mass of the two other identical fermions. This is done both for the value of the scattering length and for the function entering the Skorniakov-Ter-Martirosian integral equation, for which simple explicit expressions are obtained.

Very simple form for the solution added; conclusion added

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Cited by in corpus (7)

• Calibration of Interaction Energy between Bose and Fermi Superfluids
• Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model
• Dimer-dimer scattering length for fermions with different masses: analytical study for large mass ratio
• Atom-dimer scattering in heteronuclear mixture with finite intra-species scattering length
• Atom-dimer scattering amplitude for fermionic mixtures with different masses: s-wave and p-wave contributions
• Coboson many-body formalism for atom-dimer scattering length
• Atom-dimer and dimer-dimer scatterings in a spin-orbit coupled Fermi gas