  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.
