An experiment addressing electron capture (EC) decay of hydrogen-like $^{142}$Pm$^{60+}$ ions has been conducted at the experimental storage ring (ESR) at GSI. The decay appears to be purely exponential and no modulations were observed. Decay times for about 9000 individual EC decays have been measured by applying the single-ion decay spectroscopy method. Both visually and automatically analysed data can be described by a single exponential decay with decay constants of 0.0126(7) s$^{-1}$ for automatic analysis and 0.0141(7) s$^{-1}$ for manual analysis. If a modulation superimposed on the exponential decay curve is assumed, the best fit gives a modulation amplitude of merely 0.019(15), which is compatible with zero and by 4.9 standard deviations smaller than in the original observation which had an amplitude of 0.23(4).
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