Coboson many-body formalism for atom-dimer scattering length

TL;DR

This paper applies the coboson many-body formalism to calculate atom-dimer and dimer-dimer scattering lengths in cold fermionic gases, achieving results that closely match exact values and revealing the importance of the dimer ground state.

Contribution

It introduces the coboson formalism to cold atom physics, simplifying calculations and accurately predicting scattering lengths across various fermion mass ratios.

Findings

Accurate atom-dimer scattering lengths obtained using the coboson formalism.

The approach simplifies many-body calculations via Shiva diagrams.

Results agree well with exact values, except for a slight deviation at equal masses.

Abstract

We use the composite boson (coboson) many-body formalism to tackle scattering lengths for cold fermionic atoms. We show that bound dimers can be taken as elementary entities provided that fermion exchanges between them are treated exactly, as can be done through the coboson formalism. This alternative tool extended to cold atom physics not only makes transparent many-body processes through Shiva diagrams specific to cobosons, but also simplifies calculations. Indeed, the integral equation we derive for the atom-dimer scattering length and solve by restricting the dimer relative motion to the ground state, gives values in remarkable agreement with the exact scattering length values for all fermion mass ratios. This remarkable agreement also holds true for the dimer-dimer scattering length, except for equal fermion masses where our restricted procedure gives a value slightly larger than the accepted one ($0.64a_d$ instead of $0.60a_d$). All this proves that the scattering of a cold-atom dimer with an atom or another dimer is essentially controlled by the dimer relative-motion ground state, a physical result not obvious at first.