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We investigate the influence of the magnetic field of the  Experimental storage ring (ESR) at GSI on the periodic time-dependence of theorbital K-shell electron capture decay $(EC$) rates of the H--like heavy ions.We approximate the magnetic field of the ESR by a uniform magnetic field.Unlike the assertion by Lambiase et al., arXiv: 0811.2302 [nucl-th], we showthat a motion of the H-like heavy ion in a uniform magnetic field cannot be theorigin of the periodic time-dependence of the EC-decay rates of the H-likeheavy ions.

On the influence of the magnetic field of the GSI experimental storage ring on the time-modulation of the EC-decay rates of the H-like mother ions