Spin-rotation coupling in non-exponential decay of hydrogenlike heavy ions

We discuss a model in which a recently reported modulation in the decay of the hydrogenlike ions ${}^{140}$Pr$^{58 +}$ and ${}^{142}$Pm$^{60 +}$ arises from the coupling of rotation to the spin of electron and nuclei (Thomas precession). A similar model describes the electron modulation in muon $ g-2$ experiments correctly. Agreement with the GSI experimental results is obtained for the current QED-values of the bound electron g-factors, $g({}^{140}$Pr$^{58 +})=1.872$ and $g({}^{142}$Pm$^{60 +})=1.864$, if the Lorentz factor of the bound electron is $\sim 1.88$. The latter is fixed by either of the two sets of experimental data. The model predicts that the modulation is not observable if the motion of the ions is linear, or if the ions are stopped in a target.