Beta decay and muon capture in theA=12nuclei: Second-class currents and conserved-vector current

Abstract

A fairly detailed analysis is given of the available experimental data on ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}\to {}_{}{}^{12}{}_{}{}^{}\mathrm{C}{e}^{-}{\overline{\nu }}_e$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}\to {}_{}{}^{12}{}_{}{}^{}\mathrm{C}{e}^{+}{\nu }_e$, and ${\mu }^{-}{}_{}{}^{12}{}_{}{}^{}\mathrm{C}\to {\nu }_{\mu }{}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ making use of the "elementary-particle" treatment. Our results indicate that the variation with energy of the asymmetry coefficients obtained by Sugimoto et al. cannot be reconciled with the observed value of the muon capture rate on the hypothesis (A) of gross violation of ("strong") conserved vector current and absence of second-class axial currents and can be reconciled only with great difficulty on the alternative hypothesis (B) of validity of (strong) conserved vector current and presence of relatively large second-class axial currents. On the other hand, a good fit to the observed muon capture rate can be obtained on the hypothesis (C) of (strong) conserved vector current, ("suitably corrected") partially conserved axial vector current, and absence of second-class axial currents. This last hypothesis leads, of course, to a prediction for the variation with energy of the asymmetry coefficients in contradiction to the results of Sugimoto et al. We also find that the magnitude of the recoil ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ polarization obtained by Possoz et al. agrees with that calculated on hypothesis (C) but not with those calculated on hypotheses (A) or (B).