Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers

We derive the relativistic formulas for the van der Waals coefficients of Yb–alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate $C_6$ and $C_8$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the $C_8$ coefficient of heteronuclear $A+B$ dimers in terms of the $C_6$ and $C_8$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$. We report results of calculation of the $C_6$ coefficients for the Yb-Rb ${}^3{P}_1^o+5s{}^2{S}_{1/2}$ and ${}^1{S}_0+5p{}^2{P}_{1/2}^o$ dimers, and the $C_8$ coefficients for the Yb-Li ${}^1{S}_0+2s{}^2{S}_{1/2}$ and Yb-Rb ${}^1{S}_0+5s{}^2{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.