  Atoms are not two-level systems, and their rich internal structure often
leads to complex phenomena in the presence of light. Here, we analyze
off-resonant light scattering including the full hyperfine and magnetic
structure. We find a set of frequency detunings where the induced atomic dipole
is the same irrespective of the Zeeman state, and where two-photon transitions
that alter the atomic state turn off. For alkali atoms and alkaline-earth ions,
if the hyperfine splitting is dominated by the magnetic dipole moment
contribution, these detunings approximately coincide. Therefore, at a given
``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost
identically, and can be traced out to good approximation. This feature prevents
state decoherence due to light scattering, which impacts quantum optics
experiments and quantum information applications.
