Axial collective excitations of a degenerate Fermi gas in the BEC to unitarity crossover

We show that, with reasonable hypotheses leading to a simple modeling, a link can be obtained from experiments on the axial low-frequency collective modes between the ratio a(M)/a, of the molecular scattering length a(M) to the atomic scattering length, and the energy parameter xi equivalent to 1 + beta of the gas at the unitarity limit. We also point out that, in order to reach the range where the features of the Bose limit can be clearly seen, experiments have to go to more dilute situations than have been achieved presently.