In 2007 an ESR experiment reported the observation of unexpected modulation in time of the rate of electron capture decays of highly ionized heavy atoms — Pr, which have a lifetime of 3.39 min. Such findings were soon repeated by the same group, and were extended to include the decay of Pm (lifetime 40.5 s). The oscillations in decay rate had time periods near to 7 s and amplitudes of about 20%. Such a phenomenon had not been previously observed, and was difficult to understand. The experimental group considered it very improbable that the appearance of the phenomenon is due to a technical artefact because they report that their detection technique provides—during the whole observation time—complete and uninterrupted information upon the status of each stored ion.