Large Isospin-Mixing Matrix Element inC12

Isospin mixing between the 12.71-MeV, $1^{+}$, $T=0\mathrm{}$ and 15.11-MeV, $1^{+}$, $T=1\mathrm{}$ levels in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is measured utilizing two different direct reactions. A consistent value (${\beta }^2\sim 0.01$) is obtained from both the isospin-forbidden reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d,d^{\prime }){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ and the comparison of the yields in the analog reactions ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}\mathrm{}(d,t)\mathrm{}{}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ (15.11 MeV) and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}\mathrm{}(d,h)\mathrm{}{}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ (0.00 MeV). This mixing implies a charge-dependent matrix element between these two levels of approximately 250 keV.