Ultracold collisions between atoms and molecules in high vibrational states: effect of the atom-atom scattering length

Recently, Bose-Einstein condensates of $^6$Li$_2$ and $^{40}$K$_2$ molecules have been produced using Feshbach resonances and Pauli blocking mechanism. In these experiments, molecules are formed in the highest vibrational state and composed by fermionic atoms, and the atom-atom scattering length is large and positive. Using a quantum-mechanical formalism based on hyperspherical coordinates, we have obtained elastic and inelastic rate coefficients for the fermionic system $^6$Li + $^6$Li$_2$ and for the bosonic system $^7$Li + $^7$Li$_2$ for molecule in high vibrational states [1]. We explain the Pauli blocking mechanism that occurs in the experiments, by comparing rate coefficients for a system composed of bosonic or fermionic atoms as a function of the atom-atom scattering length. [1] G. Qu{\'e}m{\'e}ner, J.-M. Launay, and P. Honvault, Phys. Rev. A {\bf 75}, 050701(R) (2007).