Large Isospin Asymmetry in ${}^{22}\mathrm{Si}/{}^{22}\mathrm{O}$ Mirror Gamow-Teller Transitions Reveals the Halo Structure of ${}^{22}\mathrm{Al}$

$\beta$-delayed one-proton emissions of ${}^{22}\mathrm{Si}$, the lightest nucleus with an isospin projection ${\mathrm{T}}_z=-3$, are studied with a silicon array surrounded by high-purity germanium detectors. Properties of $\beta$-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 $\beta$ decay of ${}^{22}\mathrm{O}$, the largest value of mirror asymmetry in low-lying states by far, with $\delta =209(96)$, 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 $\delta$ 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.

Figure 1

Energy spectrum of $\beta$-delayed proton from ${}^{22}\mathrm{Si}$ decay measured by (a) DSSD1 ($149\mu \mathrm{m}$), (b) DSSD2 ($66\mu \mathrm{m}$). Black line and red line represent the spectra for full-energy protons and those in coincidence with $\beta$ particles detected by the downstream QSD2, respectively. Panel (c) shows the cumulative $\gamma$-ray spectrum measured by clover-type HPGe detectors in coincidence with the emitted protons from the decay of ${}^{22}\mathrm{Si}$.

Figure 2

Decay scheme of ${}^{22}\mathrm{Si}$.The transitions to 905 keV and 2145 keV are followed by the proton emissions discussed in the text, while the transition to 8829 keV is followed by a two-proton emission as discussed in Ref. [17]. All the values (except $J^{\pi }$) presented are deduced from this experiment.

Figure 3

Comparison of calculated MED with experimental data for the first (red circles) and second (blue triangles) excited $1^{+}$ states in mirror nuclei ${}^{22}\mathrm{Al}$ and ${}^{22}\mathrm{F}$.