βdecay ofB12andN12

The $\beta$ decays of ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$ to the first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been compared by detecting the $\beta$ particles in $4\pi$ geometry and simultaneously collecting $\beta -\gamma$ coincidences. All events were time sorted so that the ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$ components of the $\beta$ and $\beta -\gamma$ coincidence spectra could be accurately extracted down to low values of the $\beta$-particle energy. For the ratio of the branching ratios ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$/${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ we find 1.74 ± 0.08. This and other data are analyzed to extract the $\beta$-decay asymmetry $\left[\frac{{\mathrm{}\left(\mathrm{ft}\right)\mathrm{}}^{+}}{{\mathrm{}\left(\mathrm{ft}\right)\mathrm{}}^{-}}\right]-1=-0.013\mathrm{}\pm 0.066$. All existing data on asymmetry in Gamow-Teller $\beta$ decay in even-$A$ nuclei of the $1p$ shell are analyzed in the light of the work of Kubodera, Delorme, and Rho that, using appropriate many-body wave functions, relates the asymmetry to two fundamental second class current parameters $\zeta$ and $\lambda$. We find, at the 99% confidence limit, $\left|\zeta \right|<\mathrm{}4\mathrm{}\times {10}^{-3\mathrm{}}$ ${\mathrm{MeV}}^{-1\mathrm{}}$; $\left|\lambda \right|<\mathrm{}1.5\mathrm{}\times {10}^{-2\mathrm{}}$. In the model that ascribes all second class current effects to the $G$-parity-violating decay $\omega \to \pi e\nu$ both as an exchange term (which enters into $\lambda$) and as a nucleon decay vertex renormalization term (which determines $\zeta$ and enters into $\lambda$), our results correspond to $T_{\omega \to \pi e\nu }>5\mathrm{}\times {10}^{-11\mathrm{}}$ sec. This limit corresponds, using SU(3), to the expectation that the asymmetry in