Isospin-forbidden alpha decay of the 15.11-MeV state inC12

The branching ratio $\frac{{\Gamma }_{\alpha }}{{\Gamma }_{\mathrm{total}}}$ has been measured for the 15.11-MeV $1^{+}$ $T=1\mathrm{}$ state in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The result is $\frac{{\Gamma }_{\alpha }}{{\Gamma }_{\mathrm{total}}}=(4.1\mathrm{}\pm 0.9)$%, in agreement with one previous measurement and in disagreement with another. The result was obtained by direct observation of the decay $\alpha$ particles from the reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}\to 3\alpha$. The data are consistent with a sequential decay via the first excited state of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$. The $3\alpha$ breakup of the $1^{+}$ $T=0\mathrm{}$ state at $E_x=12.71\mathrm{}$ MeV was also studied. The data in both cases were fitted with a model in which the $\alpha -\alpha$ final state interaction was treated as a simple Breit-Wigner resonance; order-of-emission interference effects were included. If the (isospin-forbidden) $\alpha$ width is interpreted as resulting from mixing between the two $1^{+}$ states via a charge-dependent interaction, a large isospin-violating matrix element is involved.