Using sum rules techniques to calculate the radiative-pion-capture rate ${\Lambda }_{\gamma }^{\pi }\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ and the muon-capture rate ${\Lambda }_{\mu }$, two results are obtained. First, the ratio ${\Lambda }_{\gamma }^{\pi }\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ over the experimental absorption width ${\Gamma }_{\mathrm{nl}}^{\pi }$ is independent of the $\mathrm{nl}$ atomic level from which the pion is captured in each nucleus. Second, we explain the empirical observation that the radiative branching ratio scaled with the width ${\Gamma }_{1s}^{\pi }$ is nearly equal to ${\Lambda }_{\mu }$ multiplied by 2.33×${10}^{12}$. This constant is basically determined by coupling constants and masses.

• Received 23 June 1988

DOI:https://doi.org/10.1103/PhysRevC.39.302