Simple determination of Na

Abstract

\n A simple model is developed to determine a scattering length from the\nexperimental values of the energy of the last, least bound, vibrational\nlevels of the ground state, either $^1\\Sigma _g^{+}$ or $^3\\Sigma _u^{+}$,\nof an alkali dimer. It is based on an extrapolation of the positions of the\nfew outermost nodes of the bound vibrational wave functions towards the\ndissociation threshold. It uses the asymptotic part of the molecular\npotential only. The method is applied to recently measured levels at the\nasymptote (3s+3s) of Na2. We obtain precise values for the two scattering\nlengths respectively associated to the dissociation limits $F_1=F_2=1,F=2$\n(55.1±1.6 a0) and $F_1=F_2=1,F=0$ (50.0±1.6 a0); the first\nvalue corresponds to the $a_{1,-1}$ scattering length usually considered in\ncold collisions. The extrapolation procedure is also applied to Li2,\nusing existing experimental data.\n\n