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We use the composite boson (coboson) many-body formalism to tackle scatteringlengths for cold fermionic atoms. We show that bound dimers can be taken aselementary entities provided that fermion exchanges between them are treatedexactly, as can be done through the coboson formalism. This alternative toolextended to cold atom physics not only makes transparent many-body processesthrough Shiva diagrams specific to cobosons, but also simplifies calculations.Indeed, the integral equation we derive for the atom-dimer scattering lengthand solve by restricting the dimer relative motion to the ground state, givesvalues in remarkable agreement with the exact scattering length values for allfermion mass ratios. This remarkable agreement also holds true for thedimer-dimer scattering length, except for equal fermion masses where ourrestricted 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 acold-atom dimer with an atom or another dimer is essentially controlled by thedimer relative-motion ground state, a physical result not obvious at first.

Coboson many-body formalism for atom-dimer scattering length