Isospin-Forbidden Particle Decays ofT=32Levels in Mirror Nuclei

Absolute branching ratios for the isospin-forbidden particle decays of the lowest $T=\frac{3}{2}$ levels of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$ have been measured by populating the levels in (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $p$), (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $\alpha$), or (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $n$) reactions and observing the resulting decay products in coincidence. Branching ratios of 0.070 ± 0.018, 0.261 ± 0.030, and 0.026 ± 0.018 (0.236 ± 0.012, 0.150 ± 0.010, 0.053 ± 0.015) were determined for the neutron (proton) decays of the 15.1-MeV, $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$) to the ground state and first two excited states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, respectively. Branching ratios of 0.91 ± 0.15 and 0.05 ± 0.02 (0.088 ± 0.016, 0.23 ± 0.05) were determined for the neutron (proton) decays of the 11.08-(11.20-) MeV, $T=\frac{3}{2}$ level of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$) to the ground state and unresolved 6.05- and 6.13- MeV excited states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, respectively. The $\alpha$-decay branching ratios of the 15.1-MeV, $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ to the ground state and first two excited states of ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ were determined to be 0.049 ± 0.027, 0.039 ± 0.039, and 0.072 ± 0.045, respectively. Possible origins of the large asymmetries observed in the nucleon decays of these analog levels are discussed. The value obtained for $\frac{{\Gamma }_{p_0}}{\Gamma }$ for the lowest $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ may be combined with ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(e,e^{\prime })$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ measurements to determine the ratio $\frac{{\Gamma }_{\gamma }^{M1\mathrm{}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{C}\right)}{{\Gamma }_{\gamma }^{M1\mathrm{}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{N}\right)}=1.0\mathrm{}\pm 0.2$ for $\gamma$ decay to the ground state. This places an upper limit on the isotensor transition matrix element at 7% of the isovector matrix element.