  We report on the first measurement of the $\beta^+$- and orbital electron
capture decay rates of $^{140}$Pr nuclei with the most simple electron
configurations: bare nuclei, hydrogen-like and helium-like ions. The measured
electron capture decay constant of hydrogen-like $^{140}$Pr$^{58+}$ ions is
about 50% larger than that of helium-like $^{140}$Pr$^{57+}$ ions. Moreover,
$^{140}$Pr ions with one bound electron decay faster than neutral
$^{140}$Pr$^{0+}$ atoms with 59 electrons. To explain this peculiar observation
one has to take into account the conservation of the total angular momentum,
since only particular spin orientations of the nucleus and of the captured
electron can contribute to the allowed decay.
