Isospin-Forbidden Decay Properties of the LowestT=2States ofNe20,Mg24,Si28,S32, andCa40

The lowest $T=2\mathrm{}$ states of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been formed using the ($p, t$) reaction. The isospin-forbidden proton ($\Delta T=1\mathrm{} or 2$) and $\alpha$-particle ($\Delta T=2\mathrm{}$) decay modes of these states have been determined by counting triton-proton and triton-$\alpha$ coincidence events. The major decay modes of the states are ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}({\alpha }_1+{\alpha }_2, {\alpha }_3+{\alpha }_4)$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}\left(p_0\right)$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}\left({\alpha }_0\right)$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}\left(p_0\right)$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\left({\alpha }_0\right)$. Simple Coulomb calculations were performed for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$; these assumed pure shell-model configurations and considered isospin mixing in only the ($1d, 1f$) shells. They did not predict the relatively large $\Delta T=2\mathrm{}$ isospin impurities necessary to explain the observed $\alpha$-particle decay.