Radiative Muon Capture inCa40and the Induced Pseudoscalar Coupling Constant

Abstract

The process ${\mu }^{-}+p\to n+\nu +\gamma$, where $p$ is a proton in ${\mathrm{Ca}}^{40}$, was observed by detecting the $\gamma$ ray in a large NaI crystal. Only that part of the $\gamma$-ray spectrum lying above 60 MeV was analyzable because of large backgrounds at lower energies. The $\gamma$-ray spectrum is predicted theoretically to be rather sensitive to the value of $g_P$, the induced pseudoscalar coupling constant. Under the assumption that the pseudoscalar terms are induced by one-pion intermediate states only, the results of the experiment, as interpreted with the theory of Rood and Tolhoek, indicate that $g_P=(13.3\mathrm{}\pm 2.7)g_A$, where $g_A$ is the axial vector coupling constant, and the error does not include the uncertainty in the theory. This value is two standard deviations larger than the predicted value of $(7\mathrm{} or 8)g_A$. The discrepancy may be statistical or the result of inadequacies in the theory describing the process. Alternative explanations can also be found. For example, one can assume that there actually is an excess $\Delta g_P$ above that expected; assuming this excess to be independent of $q^2$ ($q=\mathrm{f}\mathrm{o}\mathrm{u}\mathrm{r}-\mathrm{m}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{u}\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{f}\mathrm{e}\mathrm{r}$) our data give $\Delta g_P=(10.4\mathrm{}\pm 5.6)g_A$. Another possible explanation would be to drop the usual assumption that the weak currents have a definite transformation character under $G$ parity, so that a tensor term (with $g_T\gtrsim 15g_V$) appears in the axial vector part of the weak current. Using the theory to extrapolate the $\gamma$-ray spectrum to low energies, a value of (3.1±0.6)×${10}^{-4\mathrm{}}$ was obtained for the ratio of radiative to ordinary muon capture. It was found that the average excitation energy given to the ${\mathrm{K}}^{40}$ nucleus is (15±4) MeV.