Large Isospin Asymmetry in Si22/O22 Mirror…

$\ensuremath{\beta}$-delayed one-proton emissions of $^{22}\mathrm{Si}$, the lightest nucleus with an isospin projection ${\mathrm{T}}_{z}=\ensuremath{-}3$, are studied with a silicon array surrounded by high-purity germanium detectors. Properties of $\ensuremath{\beta}$-decay branches and the reduced transition probabilities for the transitions to the low-lying states of $^{22}\mathrm{Al}$ are determined. Compared to the mirror $\ensuremath{\beta}$ decay of $^{22}\mathrm{O}$, the largest value of mirror asymmetry in low-lying states by far, with $\ensuremath{\delta}=209(96)$, is found in the transition to the first ${1}^{+}$ excited state. Shell-model calculation with isospin-nonconserving forces, including the $T=1$, $J=2$, 3 interaction related to the ${s}_{1/2}$ orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the ${s}_{1/2}$ orbit, can reproduce the observed data well and consistently explain the observation that a large $\ensuremath{\delta}$ value occurs for the first but not for the second ${1}^{+}$ excited state of $^{22}\mathrm{Al}$. Our results, while supporting the proton-halo structure in $^{22}\mathrm{Al}$, might provide another means to identify halo nuclei.