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The beta-delayed two-proton (beta 2p) decay of S-27 was studied using a state-of-the-art silicon array and Clover-type HPGe detectors. An energy peak at 6372(15) keV with a branching ratio of 2.4(5)% in the decay-energy spectrum was identified as a two-proton transition via the isobaric-analog state in P-27 to the ground state of Al-25 in the beta decay of S-27. Two-proton angular correlations were measured by the silicon array to study the mechanism of two-proton emission. Based on experimental results and Monte Carlo simulations, it was found that the main mechanism for the emission of beta 2p by S-27 is of sequential nature.

$\beta$ decay of $^{26}$P was used to populate the astrophysically important $E_x=$5929.4(8) keV $J^{\pi}=3{^+}$ state of $^{26}$Si. Both $\beta$-delayed proton at 418(8) keV and gamma ray at 1742(2) keV emitted from this state were measured simultaneously for the first time with corresponding absolute intensities of 11.1(12)\% and 0.59(44)\%, respectively. Besides, shell model calculations with weakly bound effects were performed to investigate the decay properties of other resonant states and a spin-parity of $4^+$ rather than $0^+$ was favored for the $E_x=$5945.9(40) keV state. Combining the experimental results and theoretical calculations, $^{25}$Al($p,\gamma$)$^{26}$Si reaction rate in explosive hydrogen burning environments was calculated and compared with previous studies.

Background: Beta-decay spectroscopy provides valuable nuclear physics input for thermonuclear reaction rates of astrophysical interest and stringent test for shell-model theories far from the stability line. Purpose: The available decay properties of proton drip-line nucleus $^{27}$S is insufficient to constrain the properties of the key resonance in $^{26}$Si$(p,\gamma)^{27}$P reaction rate and probe the possible isospin asymmetry. The decay scheme of $^{27}$S is complicated and far from being understood, which has motivated but also presented challenges for our experiment. Method: The $^{27}$S ions were implanted into a double-sided silicon strip detector array surrounded by the high-purity germanium detectors, where the $\beta$-delayed protons and $\gamma$ rays were measured simultaneously. Results: The improved spectroscopic properties including the precise half-life of $^{27}$S, the excitation energies, $\beta$-decay branching ratios, log~$ft$ values, and $B$(GT) values for the states of $^{27}$P populated in the $\beta$ decay of $^{27}$S were measured and compared to the $^{27}$Mg mirror states and the shell-model calculations. The present work has expanded greatly on the previously established decay scheme of $^{27}$S. Conclusions: The precise proton-separation energy of $^{27}$P, the energy and the ratio between $\gamma$ and proton partial widths of the $3/2^+$ resonance were obtained, thereby determining the $^{26}$Si$(p,\gamma)^{27}$P reaction rate based mainly on experimental constraints. The first evidence for the observation of a large isospin asymmetry for the mirror decays of $^{27}$S and $^{27}$Na is also provided. The experimental spectroscopic information can be reproduced by the shell-model calculation taking the weakly bound effect of the proton $1s_{1/2}$ orbit into account.