Weakly bound molecules: analysis by the Lu-Fano method coupled to the LeRoy-Bernstein model

Full text: We have performed experiments on photo-association spectroscopy of cold 87Rb atoms, below the (5s1/2+5p1/2) dissociation limit. By applying the trap loss spectroscopy method we have measured the binding energies of the weakly bound molecules, associated to the 0g- , 0u+ and 1g symmetries. Such weakly bound molecules are described by the dipole-dipole atom interaction which varies, according to the molecular symmetry, either as 1/R3 or as 1/R6, where R is the inter-nuclear distance. The eigen energies of the weakly bound molecules are then very close to those obtained by the well-known Le Roy-Bernstein (LRB) model. The discrepancies to the LRB law are due to the short distance behavior of the molecular potentials or to couplings between molecular potentials resulting from interactions, for example spin-orbit or spin-spin interactions. To analyze the data, we have adapted the Lu-Fano (LF) method - well-known for Rydberg atoms - to the weakly bound molecules. Using the LRB law, a molecular quantum defect is defined and deduced from the data. The LF graph - quantum defect versus the binding energy - allows us to characterize the molecular potential and the couplings. For the 0g- molecular levels, we observe a linear LF graph, which is the signature of the short range behavior of the molecular potential. A model for the barrier allows us to connect the slope to the barrier location. The method has also been applied to 85Rb and 133Cs. For 0u+ molecular levels, the LF graph exhibits sharp variations which indicate a coupling with a neighboring molecular series. The coupling is due to the spin-orbit interaction in the molecule. A two series model allows us to evaluate the coupling, to identify two perturbing levels of the (5s1/2+5p3/2) 0u+ series and to predict the energy position and the width of its first pre-dissociated level. An experimental signal agrees with the prediction. The method has also been successfully applied to 133Cs. (author)