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We show that by averaging over transitions to multiple hyperfine levels,quadrupole shifts and dominant Zeeman effects exactly cancel whenever thenuclear spin, I, is at least as large as the total electronic angular momentum,J. The average frequency thus defines a frequency reference which is inherentlyindependent of external magnetic fields and electric field gradients. We useLu+ to illustrate the method although the approach could be readily adapted toother atomic species. This approach practically eliminates the quadrupole andZeeman shift considerations for many clock candidates.

Developing a field independent frequency reference by averaging over transitions to multiple hyperfine levels