Polarizabilities and tune-out wavelengths of the hyperfine ground states of ${}^{87,85}$Rb

The static and dynamic polarizabilities, and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of ${}^{87,85}$Rb have been calculated by using relativistic configuration interaction plus core polarization(RCICP) approach. It is found that the first primary tune-out wavelengths of the $5s_{1\mathrm{/}2},F=1,2$ states of ${}^{87}$Rb are 790.018187(193) nm and 790.032602(193) nm severally, where the calculated result for the $5s_{1\mathrm{/}2},F=2$ state is in good agreement with the latest high-precision measurement 790.032388(32) nm [Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the $5s_{1\mathrm{/}2},F=2,3$ states of ${}^{85}$Rb are 790.023515(218) nm and 790.029918(218) nm respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels $M_F$ of each hyperfine level $F$ are also determined by considering the contributions of tensor polarizabilities.