Using first-principles calculations, we identify magic wavelengths ${\lambda }_{\mathrm{magic}}$ for the $2s$-$2p$ and $2s$-$3p$ transitions in lithium. The $ns$ and $np$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between ${}^6$Li and ${}^7$Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the $2s$, $2p$, $3s$, $3p$, and $3d$ levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv $2s$-$3p$ transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].

• Received 8 August 2012

DOI:https://doi.org/10.1103/PhysRevA.86.042505