The photon energy spectra from radiative muon capture on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been measured using a time projection chamber as a pair spectrometer. The branching ratio for radiative muon capture is sensitive to ${\mathit{g}}_{\mathit{p}}$, the induced pseudoscalar coupling constant of the weak interaction. Expressed in terms of the axial-vector weak coupling constant ${\mathit{g}}_{\mathit{a}}$, values of ${\mathit{g}}_{\mathit{p}}$/${\mathit{g}}_{\mathit{a}}$=5.7±0.8 and ${\mathit{g}}_{\mathit{p}}$/${\mathit{g}}_{\mathit{a}}$=7.3±0.9 are obtained for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, respectively, from comparison with phenomenological calculations of the nuclear response. From comparison with microscopic calculations, values of ${\mathit{g}}_{\mathit{p}}$/${\mathit{g}}_{\mathit{a}}$=4.6±1.8, 13.$6_{\mathrm{-}1.9}^{+1.6\mathrm{}}$, and 16.$2_{\mathrm{-}0.7}^{+1.3\mathrm{}}$ for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, respectively, are obtained. The microscopic results are suggestive of a renormalization of the nucleonic form factors within the nucleus.

• Received 9 May 1990

DOI:https://doi.org/10.1103/PhysRevC.43.1425