Magic and tune-out wavelengths for atomic francium

@article{Dammalapati2016MagicAT,
  title={Magic and tune-out wavelengths for atomic francium},
  author={Umakanth Dammalapati and Kenji Harada and Yasuhiro Sakemi},
  journal={Physical Review A},
  year={2016},
  volume={93},
  pages={043407}
}
The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s$ $^{2}{S}_{1/2}$, $7p$ $^{2}{P}_{1/2,3/2}$, and $8s$ $^{2}{S}_{1/2}$ levels of the $7s$ $^{2}{S}_{1/2}\ensuremath{-}7p$ $^{2}{P}_{1/2,3/2}$ and $7s$ $^{2}{S}_{1/2}\ensuremath{-}8s$ $^{2}{S}_{1/2}$ transitions, respectively… 

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