On the time modulation of the K-shell electron capture decay rates of H-like heavy ions at GSI experiments

According to experimental data at GSI, the rates of the number of daughter ions, produced by the nuclear K-shell electron capture (EC) decays of the H-like heavy ions with one electron in the K-shell, such as 142Pr58+, 142Pm60+ and 122I52+, are modulated in time with periods T_(EC)of the order of a few seconds, obeying an A-scaling T_(EC)= A/20 s, where A is the mass number of the mother nuclei, and with amplitudes a^(EC)_d ~ 0.21. We show that these data can be explained in terms of the interference of two massive neutrino mass-eigenstates. The appearance of the interference term is due to overlap of massive neutrino mass-eigenstate energies and of the wave functions of the daughter ions in two-body decay channels, caused by the energy and momentum uncertainties introduced by time differential detection of the daughter ions in GSI experiments.