Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium

We have studied magnetic Feshbach resonances in an ultracold sample of Na prepared in the absolute hyperfine ground state. We report on the observation of three $s$-, eight $d$-, and three $g$-wave Feshbach resonances, including a more precise determination of two known $s$-wave resonances, and one $s$-wave resonance at a magnetic field exceeding 200 mT. Using a coupled-channels calculation we have improved the sodium ground-state potentials by taking into account these new experimental data and derived values for the scattering lengths. In addition, a description of the molecular states leading to the Feshbach resonances in terms of the asymptotic-bound-state model is presented.