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Weak decays of H-like<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi /><mml:mrow><mml:mn>140</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi mathvariant="normal">Pr</mml:mi><mml:mrow><mml:mn>58</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>and He-like<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi /><mml:mrow><mml:mn>140</mml:mn></mml:mrow></mml:msup><mml:msup><mml…
The nuclear $K$-shell electron-capture (EC) and positron (${\ensuremath{\beta}}^{+}$) decay constants, ${\ensuremath{\lambda}}_{\mathrm{EC}}$ and ${\ensuremath{\lambda}}_{{\ensuremath{\beta}}^{+}}$ of H-like ${}^{140}{\mathrm{Pr}}^{58+}$ and He-like ${}^{140}{\mathrm{Pr}}^{57+}$ ions, measured recently in the experimental storage ring (ESR) at GSI, were calculated using standard weak interaction theory. The calculated ratios $R={\ensuremath{\lambda}}_{\mathrm{EC}}/{\ensuremath{\lambda}}_{{\ensuremath{\beta}}^{+}}$ of the decay constants agree with the experimental values …