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In the relativistic description of atomic systems in external fields thetotal momentum and the external electric field couple to the angular momentumof the individual particles. Therefore, the motional state of an ion in aparticle trap influences measurements of internal observables like energylevels or the g-factor. We calculate the resulting relativistic shift of theLarmor frequency and the corresponding g-factor correction for a bound electronin a hydrogen-like ion in the 1S state due to the ion moving in a Penning trapand show that it is negligible at the current precision of measurements. Wealso show that the analogous energy shift for measurements with an ion in theground state of a Paul trap vanishes in leading order.

Influence of ion movement on the bound electron g-factor