Total decay rate of a muon bound to a light nucleus

TL;DR

This paper reevaluates the decay rate of a muon bound to light nuclei, resolving previous discrepancies by improving the convergence of relativistic calculations and confirming the validity of perturbative expansions.

Contribution

It provides a more accurate relativistic calculation of muon decay rates in light nuclei, clarifying the source of past discrepancies and confirming the sign of higher-order corrections.

Findings

Relativistic calculations agree with perturbative expansions.

Discrepancies from earlier work are due to partial-wave series convergence issues.

Next-order $( ext{alpha Z})^3$ correction is negative.

Abstract

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.