Tune-out and magic wavelengths of \nBa+\n ions

Abstract

The static and dynamic polarizabilities of the ground state and low-lying excited states of ${\\mathrm{Ba}}^{+}$ ions are calculated by using a relativistic semiempirical method: the relativistic configuration interaction plus core polarization (RCICP) method. The tune-out wavelengths of the ground state and magic wavelengths of the $6{s}_{1/2}\\ensuremath{\\rightarrow}6{p}_{1/2,3/2},5{d}_{3/2,5/2}$ transitions are determined. One visible tune-out wavelength, 480.658(18) nm, is found. High-precision measurements on this tune-out wavelength could be used to determine the ratio of the oscillator strengths of the $6{s}_{1/2}\\ensuremath{\\rightarrow}6{p}_{1/2,3/2}$ transitions. In addition, we suggest that the measurements on the magic wavelengths corresponding to the $6{s}_{1/2}\\ensuremath{\\rightarrow}5{d}_{3/2,5/2}$ transitions could be used to determine the oscillator strengths of the $5{d}_{5/2}\\ensuremath{\\rightarrow}4{f}_{7/2}$ and $5{d}_{3/2}\\ensuremath{\\rightarrow}4{f}_{5/2}$ transitions, while the measurements of the magic wavelengths near 416 nm for the $6{s}_{1/2}\\ensuremath{\\rightarrow}6{p}_{3/2}$ transition could be used to determine the ratio of the oscillator strengths of the $6{p}_{3/2}\\ensuremath{\\rightarrow}6{d}_{3/2,5/2}$ transitions.