Isospin-forbidden particle decays of T = 3/2 levels in mirror nuclei

Absolute branching ratios for the isospin-forbidden particle decays of the lowest T=3/2 levels of ¹³C, ¹³N, ¹⁷O, and ¹⁷F have been measured by populating the levels in (³He, p), (³He, α), or (³He, 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=3/2 level of ¹³C(¹³N) to the ground state and first two excited states of ¹²C, 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=3/2 level of ¹⁷O(¹⁷F) to the ground state and unresolved 6.05- and 6.13- MeV excited states of ¹⁶O, respectively. The α-decay branching ratios of the 15.1-MeV, T=3/2 level of ¹³N to the ground state and first two excited states of ⁹B 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=3/2 level of ¹³N may be combined with ¹³C(e,e′) and ¹²C(p,γ)¹³N measurements to determine the ratio $\frac{{\Gamma }_{\gamma }^{M1}{(}^{13}C)}{{\Gamma }_{\gamma }^{M1}{(}^{13}N)}=1.0\pm 0.2$ for γ decay to the ground state. This places an upper limit on the isotensor transition matrix element at 7% of the isovector matrix element.