Long-range potentials for two-species alkali-metal atoms

We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}-n^{\prime }S,nS-n^{\prime }P,nS-n^{\prime }D,$ and $\mathrm{nP}-n^{\prime }P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}\mathrm{}\left(5S\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6S\right),\mathrm{Rb}\mathrm{}\left(6S\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6S\right),\mathrm{K}\mathrm{}\left(4S\right)\mathrm{}-\mathrm{R}\mathrm{b}\mathrm{}\left(5P\right)\mathrm{}{\hspace{0.5em}}^{1,3}\Sigma ,\mathrm{K}\mathrm{}\left(4P\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6P\right)\mathrm{}{\hspace{0.5em}}^{1,3}\Sigma ,$ and $\mathrm{Rb}\mathrm{}\left(5S\right)\mathrm{}-\mathrm{N}\mathrm{a}\mathrm{}\left(3D\right)\mathrm{}{\hspace{0.5em}}^{1,3}\Sigma$ molecules to be the most attractive. The $\mathrm{K}\mathrm{}\left(4S\right)\mathrm{}-\mathrm{R}\mathrm{b}\mathrm{}\left(5P\right)\mathrm{}$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}\mathrm{}\left(4P\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6P\right)\mathrm{}$ and $\mathrm{Rb}\mathrm{}\left(5S\right)\mathrm{}-\mathrm{K}\mathrm{}\left(4P\right)\mathrm{}$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the ${1/R}^6$ van der Waals coefficient for the interaction between $\mathrm{Cs}\mathrm{}\left(6S\right)\mathrm{}$ and $\mathrm{Li}\mathrm{}\left(2P\right)\mathrm{}$ atoms.