Determination of collisional properties of cold Na atoms from analysis of bound-state photoassociation and Feshbach resonance field data

Abstract

We review the information on the interactions between cold ground-state Na atoms following from ${\mathrm{Na}}_{2}$ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length ${a}_{1,\ensuremath{-}1}$ of Na atoms in the $|1,\ensuremath{-}1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths ${a}_{S}$ and ${a}_{T},$ ${a}_{1,\ensuremath{-}1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find ${a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},$ and ${a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.$