Time Modulation of the {beta}{sup +}-Decay Rate of H-Like {sup 140}Pr{sup 58+} Ions

Recent experimental data at GSI on the rates of the number of daughter ions, produced by the nuclear K-shell electron capture (EC) decays of the H-like ions {sup 140}Pr{sup 58+} and {sup 142}Pm{sup 60+}, suggest that they are modulated in time with periods T{sub EC}{approx_equal}7 sec and amplitudes a{sub EC}{approx_equal}0.20. Since it is known that these ions are unstable also under the nuclear positron ({beta}{sup +}) decays, we study a possible time dependence of the nuclear {beta}{sup +}-decay rate of the H-like {sup 140}Pr{sup 58+} ion. We show that the time dependence of the {beta}{sup +}-decay rate of the H-like {sup 140}Pr{sup 58+} ion as well as any H-like heavy ions cannot be observed.