Radiative muon capture on carbon, oxygen and calcium

The partial branching ratio for photons of greater than 57 MeV (G[sub >57]) has been measured for radiative muon capture (RMC) on ¹²C, ¹⁶O and ⁴⁰Ca in order to determine the magnitude of the induced pseudoscalar coupling constant g[sub p] of the weak hadronic current. A time projection chamber (TPC) was used as a large solid-angle, medium-resolution pair spectrometer to detect the photons from RMC. The resulting spectra were essentially background-free, allowing a determination of the partial branching ratios to about 10% precision. For ⁴⁰Ca, the partial branching ratio obtained is in good agreement with previous measurements, and yields the value g[sub p]/g[sub a] = 5.7 ± 0.8 when compared with a phenomenological calculation of the nuclear response function and the value g[sub p]/g[sub a] = 4.6 ± 1.8 when compared with a microscopic calculation of the nuclear response function. Both of these results suggest a slight (downward) renormalization of g[sub p]/g[sub a] in ⁴⁰Ca in comparison with the value expected for a free nucleoli. For ¹⁶O, the partial branching ratio obtained in the present experiment is found to disagree strongly with one previous experiment but to agree with the second previous measurement. When compared with a phenomenological calculation of the nuclear response our result yields g[sub p]/g[sub a] = 7.3 ± 0.9, consistent with an un-renormalized value of g[sub p]. The same results compared to a microscopic calculation give the value g[sub p]/g[sub a] = 13.6 [sup +1.6]/[sub -1.9] suggesting a large (upward) renormalization of g[sub p] in the ¹⁶O nucleus. The first precise branching ratio has also been measured for RMC on ¹²C. No calculation of the nuclear response specific to ¹²C is available at present. However, when the present data are compared with a naive extrapolation of Fermi-gas model calculations of the nuclear response for heavier nuclei, the brandling ratio is found to be consistent with an unrenormalized value of g[sub p]. The present work has also provided valuable input, through the investigation of various systematic errors and potential backgrounds, into the design of a detection system for a forthcoming measurement of RMC on hydrogen.Science, Faculty ofPhysics and Astronomy, Department ofGraduat