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 2S1/2,
7p 2P1/2,3/2, and
8s 2S1/2 levels of the
7s $^{2}{S}_{1/2}\ensuremath{-}7p$
2P1/2,3/2 and
7s $^{2}{S}_{1/2}\ensuremath{-}8s$
2S1/2 transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600--700 nm and 700--1000 nm regions, which are blue and red detuned with the $7s\ensuremath{-}7p$ and $7s\ensuremath{-}8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground
7s 2S1/2 state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.
Summary form only given. Atomic lifetime measurements are important probes of atomic structure because they depend on the initial and final state wave functions and the interaction that connects them. The study of francium, the heaviest alkali, has two advantages over other heavy elements. It has a simple atomic structure to calculate accurately, and it is possible to trap it with the well developed techniques of laser trapping and cooling despite the fact that its longest-lived isotope has a half-life of 20 minutes. Francium has the potential to increase our understanding of relativistic atoms while at the same time providing a good candidate for tests of the fundamental symmetries of parity and time in a calculable atomic system.