Cold atomic collisions studied by molecular spectroscopy

We observe bound states just below the dissociation limit and shape and Feshbach resonances between the ground state hyperfine asymptotes by Raman spectroscopy on a molecular beam of sodium dimers. The rotational selectivity of a two-photon transition gives access to specific states of nuclear motion and thus to cold collision properties of two colliding atoms. Modeling of the collisional resonance structures requires a multichannel treatment of the nuclear dynamics that uses highly accurate $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potentials. These potentials are constructed from bound levels just below the ground state asymptote measured in this experiment and bound state information available in the literature. We also present simulations of the spectrum between the ground state hyperfine asymptotes. The good agreement shows that accurate potentials obtained from bound state information are able to reproduce scattering properties of two colliding sodium atoms. From this analysis we find for the scattering lengths ${a(f=2)=a}_{1,\ensuremath{-}1}{=52.98(40)a}_{0},$ ${a}_{\mathrm{singlet}}{=19.20(30)a}_{0},$ and ${a}_{\mathrm{triplet}}{=62.51(50)a}_{0},$ where ${1a}_{0}=0.0529177$ nm.