Radiative transitions and isospin mixing inC12

Abstract

$\ensuremath{\gamma}$-ray decays of the 12.7 and 16.1 MeV states of $^{12}\mathrm{C}$ are investigated in a coincidence study of the $^{10}\mathrm{B}(^{3}\mathrm{He}, p\ensuremath{\gamma})$ reaction. We obtain $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{\ensuremath{\Gamma}}=(1.93\ifmmode\pm\else\textpm\fi{}0.12)%$, $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}=(15.0\ifmmode\pm\else\textpm\fi{}1.8)%$ and $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\alpha}}}{\ensuremath{\Gamma}}=(97.8\ifmmode\pm\else\textpm\fi{}0.1)%$ for $^{12}\mathrm{C}$(12.7), and $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}{\ensuremath{\Gamma}}=(2.42\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for $^{12}\mathrm{C}$(16.1). Relative $\ensuremath{\gamma}$-ray branching ratios of $^{12}\mathrm{C}$(16.1) were measured using the ${E}_{p}=163$ keV $^{11}\mathrm{B}(p, \ensuremath{\gamma})$ resonance. We find $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}=(4.6\ifmmode\pm\else\textpm\fi{}0.7)%$, $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}(16.1\ensuremath{\rightarrow}9.6)}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}=(2.4\ifmmode\pm\else\textpm\fi{}0.4)%$, and $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}(16.1\ifmmode\pm\else\textpm\fi{}12.7)}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}=(1.46\ifmmode\pm\else\textpm\fi{}0.25)%$. This information, together with existing data on $M1$ transitions and single nucleon transfer reactions, is used to determine the isospin mixing between the 12.7 and 15.1 MeV levels of $^{12}\mathrm{C}$. A charge dependent matrix element of 110 \ifmmode\pm\else\textpm\fi{} 30 keV is deduced.NUCLEAR REACTIONS $^{10}\mathrm{B}(^{3}\mathrm{He}, p\ensuremath{\gamma})$, $E=4.1$ MeV, $p$, $\ensuremath{\gamma}$ coincidence. Deduced ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ for $^{12}\mathrm{C}$ levels at 12.7, 16.1 MeV. $^{11}\mathrm{B}(p, \ensuremath{\gamma})$, $E=163$ keV resonance. Measured ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ for transitions to 0.0, 4.4, 9.6, and 12.7 MeV in $^{12}\mathrm{C}$.NUCLEAR STRUCTURE $^{12}\mathrm{C}$, deduced isospin mixing between 12.7 and 15.1 MeV levels.