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 ≤ Z ≤ 9 . The discrepancy between the perturbative ( α Z ) 2 result in H. Überall and the fully relativistic partial-wave calculation of R. Watanabe 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 α Z expansion and indicate a negative sign for the next-order ( α Z ) 3 correction.