Elastic scattering of two Na atoms

Interaction potentials for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ states of ${\mathrm{Na}}_2$ are constructed and used in calculations of the elastic scattering of two Na atoms at ultralow temperatures. The sensitivity to retardation effects (or Casimir corrections) is explored. The calculated elastic and spin-change cross sections are very large, of the order of ${10}^{\mathrm{-}12}$–${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^2$ at zero temperature. The predicted scattering lengths are both positive, 34.9 ${\mathit{a}}_0$ for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ state and 77.3 ${\mathit{a}}_0$ for the a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ state. Pronounced shape resonances appear for the l=3 and 7 partial waves for the singlet and l=6 for the triplet states.