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The multiphoton resonance transitions between ground hyperfine states areused for the time modulation of the electron capture decay of hydrogen likeions with the Gamow-Teller transition $1^+\to 0^+$. The proposed mechanismoffers a time oscillating decay with the frequency up to 0.1 Hz. The experimentto observe the modulation is proposed for ions stored in a Penning trap. Anattempt to understand the GSI anomaly with multiple photon transitions is made.

Time Modulation of K-electron Capture Decay of Hydrogen-Like Ions with Multiphoton Resonance Transitions