Simultaneous measurement of $\beta$-delayed proton and $\gamma$ emission of ${}^{26}\mathrm{P}$ for the ${}^{25}\mathrm{Al}(p,\gamma ){}^{26}\mathrm{Si}$ reaction rate

The $\beta$ decay of ${}^{26}\mathrm{P}$ was used to populate the astrophysically important $E_x=5929.4\left(8\right)$ keV, $J^{\pi }=3{}^{+}$ state of ${}^{26}\mathrm{Si}$. Both $\beta$-delayed protons at 418(8) keV and $\gamma$ rays at 1742(2) keV emitted from this state were measured simultaneously for the first time, and the corresponding absolute intensities have been estimated as 11.1(12)% and 0.59(44)%, respectively. The half-life of ${}^{26}\mathrm{P}$ has been determined to be 43.6(3) ms, which is in good agreement with previous experimental results. 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 $0^{+}$ is favored for the $E_x=5945.9\left(40\right)$ keV state. Combining the experimental results and theoretical calculations, the ${}^{25}\mathrm{Al}(p,\gamma ){}^{26}\mathrm{Si}$ reaction rate in explosive hydrogen burning environments was calculated. The new determined total reaction rate is consistent with previous studies at $T>0.2$ GK.

Figure 1

ToF-$\mathrm{\Delta }E$ two-dimensional spectrum measured by the plastic scintillators (T1 and T2) and one of the quadrant silicon detectors ($\mathrm{\Delta }E1$). Heavy ions are marked with red (gray) circles and the corresponding isotope symbols. The color scale represents the number of ions.

Figure 2

Schematic layout of the detection setup.

Figure 3

The decay-time spectrum of ${}^{26}\mathrm{P}$ was obtained by the time differences between the implantation of ${}^{26}\mathrm{P}$ and all the subsequent decay events within a time window of 500 ms. An exponential decay component (blue short-dashed line) and a constant background component (green long-dashed line) are applied in the fitting to determine the half-life and estimate the background.

Figure 4

Low-energy part of the cumulative $\beta$-delayed charged-particle spectrum from the $\beta$ decay of ${}^{26}\mathrm{P}$. Proton peaks are labeled as $p_1$ to $p_5$ with the corresponding center-of-mass energy in keV. The $\beta$ pile-up effects are strongly suppressed by the anticoincidence of $\beta$ signals from QSD1.

Figure 5

(a) The cumulative $\gamma$-ray spectrum measured by HPGe detectors that are gated by the $\beta$ particles in DSSD3. (b) $\gamma$-ray spectrum from 1720 to 1780 keV.

Figure 6

Proton-capture reaction rates of ${}^{25}\mathrm{Al}{(p,\gamma )}^{26}\mathrm{Si}$. The red (gray) shadow area is the upper and lower limits of the total reaction rate. Nonresonant and resonant reaction rates are presented in different colored lines.

Figure 7

Ratios of the present total ${}^{25}\mathrm{Al}{(p,\gamma )}^{26}\mathrm{Si}$ reaction rate to the literature values [12, 16, 17, 51] in the JINA REACLIB database [53]. The red (gray) shadow area shows the upper and lower limits in this work.