Role of the atom-atom scattering length and of symmetrization in unidimensional ultracold atom-diatom collisions

The role of the atom-atom scattering length and of the symmetrization in ultracold atom-diatom collisions in one dimension is presented. For an ultracold atom-diatom collision and for a diatomic molecule in its highest vibrational state, inelastic rate coefficients vanish for a system composed of fermionic atoms as the atom-atom scattering length increases whereas they do riot for a system composed of bosonic atoms. The differences come from the symmetrization of the wavefunction of the systems. We explain these differences by comparing the shape of the effective potentials of the atom-diatom approach. For the fermionic system, we use a zero-range interaction to modelize the adiabatic energies and we give a lower estimate of the atom-diatom scattering length as a function of the atom-atom scattering length.