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Atoms are not two-level systems, and their rich internal structure oftenleads to complex phenomena in the presence of light. Here, we analyzeoff-resonant light scattering including the full hyperfine and magneticstructure. We find a set of frequency detunings where the atomic induced dipoleis the same irrespective of the magnetic state, and where two-photontransitions that alter the atomic state turn off. For alkali atoms andalkaline-earth ions, if the hyperfine splitting is dominated by the magneticdipole moment contribution, these detunings approximately coincide. Therefore,at a given ``magical'' detuning, all magnetic states in a hyperfine manifoldbehave almost identically, and can be traced out to good approximation. Thisfeature prevents state decoherence due to light scattering, which impactsquantum optics experiments and quantum information applications.

State-insensitive wavelengths for light shifts and photon scattering from Zeeman states