LAUSR

The dynamic dipole polarizabilities of low-lying states of ${\mathrm{Ca}}^{+}$ ions for circularly polarized light are calculated by using the relativistic configuration interaction plus core polarization approach. The magic wavelengths are determined for the magnetic sublevel transitions $4{s}_{\frac{1}{2},m}\ensuremath{\rightarrow}4{p}_{{j}^{\ensuremath{'}},{m}^{\ensuremath{'}}}$ and $4{s}_{\frac{1}{2},m}\ensuremath{\rightarrow}3{d}_{{j}^{\ensuremath{'}},{m}^{\ensuremath{'}}}$ with total angular momentum ${j}^{\ensuremath{'}}$ and its components ${m}^{\ensuremath{'}}$. In contrast to the case of linearly polarized light, several additional magic wavelengths are found for these transitions. We suggest that accurate measurements on the magic wavelengths near 851 nm for the $4{s}_{\frac{1}{2},m}\ensuremath{\rightarrow}4{p}_{\frac{3}{2},{m}^{\ensuremath{'}}}$ transitions can be used to determine the ratio of the oscillator strengths for the $4{p}_{\frac{3}{2}}\ensuremath{\rightarrow}3{d}_{\frac{3}{2}}$ and $4{p}_{\frac{3}{2}}\ensuremath{\rightarrow}3{d}_{\frac{5}{2}}$ transitions.