Total decay rate of a muon bound to a light nucleus

We revisit the total decay rate of a muon being in the ground state of a Coulomb potential with atomic charge numbers $4\leq Z \leq 9$. The discrepancy between the perturbative $(\alpha Z)^2$ result of [Phys. Rev. \textbf{119}, 365 (1960)] and the fully relativistic partial-wave calculation of [At. Data Nucl. Data Tables \textbf{54}, 165 (1993)] for oxygen ($Z=8$) is shown to originate from insufficient convergence of the partial-wave series in the latter work. Our accurate relativistic calculations restore agreement with the perturbative $\alpha Z$~expansion and indicate a negative sign for the next-order $(\alpha Z)^3$ correction.