Mixture of composite-boson molecules and the Pauli exclusion principle

Molecules made of two fermionic atoms are 'cobosons' - a contraction for 'composite bosons'. These molecules 'feel' each other not only through interactions between atoms, but also through the Pauli exclusion between their fermionic components. In order to point out the importance of this Pauli exclusion in cold atom physics, we have calculated here the energy change of N identical cobosonic molecules when a similar molecule, made of atoms having possibly different spin states, is added. Due to the difference in the number of fermion exchanges with a molecule having zero, one, or two atoms identical to the ones already present in the system, we may think that this energy change can take three different values, even for spin-independent interatomic interactions. We actually find that the energy change, in the Born approximation, is exactly the same at all orders in density, when the added molecule has two or just one atom identical to the ones already there. In other words, the scattering length is predicted to be the same if the added molecule can have exchanges with one set of fermionic components or with two sets. This unexpected equality, which of course holds for spin-independent interactions only, results from a subtle balance in the fermion exchanges. To prove it, we make use of a recent extension of the composite-exciton many-body theory we have constructed, to any type of cobosons, the physical understanding of the various exchange processes being enlightened by the Shiva diagram representation (so named because of the multiarm structure reminiscent of the Hindu god Shiva) of this many-body theory