  Using first-principles calculations, we identify "magic-zero" optical
wavelengths, \lambda_zero, for which the ground-state frequency-dependent
polarizabilities of alkali-metal atoms vanish. 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. We discuss the use of magic-zero wavelengths for
sympathetic cooling in two-species mixtures of alkalis with group-II and other
elements of interest. Special cases in which these wavelengths coincide with
strong resonance transitions in a target system are identified.
