Elastic scattering of twoLi7atoms

Interaction potentials for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ states of ${\mathrm{Li}}_2$ are constructed and used in calculations of the elastic scattering of two ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms at ultralow temperatures. The extreme sensitivity of the cross sections to the details of the interaction potentials is demonstrated. The calculated elastic and spin-change cross sections are very large, of the order of ${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^2$ at zero temperature. The predicted scattering length for the triplet state is negative with a value of -17.2${\mathit{a}}_0$. Pronounced shape resonances appear at energies of 4.9×${10}^{\mathrm{-}8}$ a.u. in the singlet scattering and 5.5×${10}^{\mathrm{-}7}$ a.u. in the triplet scattering.