Abstract
The multiphoton resonance transitions between ground hyperfine states are used for the time modulation of the electron capture decay of hydrogen like ions with the Gamow-Teller transition $1^+\to 0^+$. The proposed mechanism offers a time oscillating decay with the frequency up to 0.1 Hz. The experiment to observe the modulation is proposed for ions stored in a Penning trap. An attempt to understand the GSI anomaly with multiple photon transitions is made.
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