Eur. Phys. J. D 6, 211-220 (1999)
https://doi.org/10.1007/s100530050303

Simple determination of Na₂ scattering lengths using observed bound levels at the ground state asymptote

¹ Laboratoire Aimé Cotton, CNRS II, bât. 505, Campus d'Orsay, 91405 Orsay, France
² Institut für Quantenoptik, Universität Hannover, 30167 Hannover, Germany

Received: 28 September 1998
Revised: 21 December 1998
Published online: 15 May 1999

Abstract

A simple model is developed to determine a scattering length from the experimental values of the energy of the last, least bound, vibrational levels of the ground state, either or , of an alkali dimer. It is based on an extrapolation of the positions of the few outermost nodes of the bound vibrational wave functions towards the dissociation threshold. It uses the asymptotic part of the molecular potential only. The method is applied to recently measured levels at the asymptote (3s+3s) of Na₂. We obtain precise values for the two scattering lengths respectively associated to the dissociation limits (55.1±1.6 a₀) and (50.0±1.6 a₀); the first value corresponds to the scattering length usually considered in cold collisions. The extrapolation procedure is also applied to Li₂, using existing experimental data.