Observation of a Strongly Isospin-Mixed Doublet in ${}^{26}\mathrm{Si}$ via $\beta$-Delayed Two-Proton Decay of ${}^{26}\mathrm{P}$

$\beta$ decay of proton-rich nuclei plays an important role in exploring isospin mixing. The $\beta$ decay of ${}^{26}\mathrm{P}$ at the proton drip line is studied using double-sided silicon strip detectors operating in conjunction with high-purity germanium detectors. The $T=2$ isobaric analog state (IAS) at 13 055 keV and two new high-lying states at 13 380 and 11 912 keV in ${}^{26}\mathrm{Si}$ are unambiguously identified through $\beta$-delayed two-proton emission ($\beta 2p$). Angular correlations of two protons emitted from ${}^{26}\mathrm{Si}$ excited states populated by ${}^{26}\mathrm{P}$ $\beta$ decay are measured, which suggests that the two protons are emitted mainly sequentially. We report the first observation of a strongly isospin-mixed doublet that deexcites mainly via two-proton decay. The isospin mixing matrix element between the ${}^{26}\mathrm{Si}$ IAS and the nearby 13 380-keV state is determined to be 130(21) keV, and this result represents the strongest mixing, highest excitation energy, and largest level spacing of a doublet ever observed in $\beta$-decay experiments.

Figure 1

Energy spectra of $\beta$-delayed protons from the decay of ${}^{26}\mathrm{P}$ measured by (a) DSSD3 ($304\mathrm{\mu }\mathrm{m}$) and (b) DSSD2 ($40\mathrm{\mu }\mathrm{m}$), respectively. (c) $\gamma$-ray spectrum measured by Clover detectors in coincidence with $\beta$-delayed protons of ${}^{26}\mathrm{P}$ in DSSD3. (d) Charged-particle spectrum acquired by DSSD3 in coincidence with the 1369-keV ${}^{24}\mathrm{Mg}$ $\gamma$ ray. Each $\gamma$ peak is labeled by the emitting nucleus and its energy rounded to the closest integer in units of keV. The proton peaks labeled with an asterisk (*) are first observed in this Letter.

Figure 2

Two-proton decay energy spectrum of the events, in which two protons escaped from the implantation detector DSSD2 and were detected by the adjacent DSSD1 and/or DSSD3.

Figure 3

Distributions of the opening angle of two protons at (a) 5277 keV and (b) combined energies of 3902, 4125, and 4250 keV in Fig. 2. The colored curves are simulation results assuming sequential emission and the black dots are experimental results in the present Letter.

Figure 4

Partial decay scheme of ${}^{26}\mathrm{P}$ deduced from the present Letter. The $S_p$ and $S_{2p}$ of ${}^{26}\mathrm{Si}$ are adopted from Ref. [33]. The black, blue, and red arrows represent transitions from the initial states of IAS, 11 912 keV, and 13 380 keV, respectively. The $I_{\beta }$ and log $ft$ value of the first excited state ($J^{\pi }=2^{+}$) in ${}^{26}\mathrm{Si}$ are adopted from Ref. [25].