${}^{25}\mathrm{Si}{\beta }^{+}$-decay spectroscopy

Background: $\beta$-decay spectroscopy provides valuable information on exotic nuclei and a stringent test for nuclear theories beyond the stability line.

Purpose: To search for new $\beta$-delayed protons and $\gamma$ rays of ${}^{25}\mathrm{Si}$ to investigate the properties of ${}^{25}\mathrm{Al}$ excited states.

Method: ${}^{25}\mathrm{Si}\beta$ decays were measured by using the Gaseous Detector with Germanium Tagging system at the National Superconducting Cyclotron Laboratory. The protons and $\gamma$ rays emitted in the decay were detected simultaneously. A Monte Carlo method was used to model the Doppler broadening of ${}^{24}\mathrm{Mg}\gamma$-ray lines caused by nuclear recoil from proton emission. Shell-model calculations using two newly developed universal sd-shell Hamiltonians were performed.

Results: The most precise ${}^{25}\mathrm{Si}$ half-life to date has been determined. A new proton branch at 724(4) keV and new proton-$\gamma$-ray coincidences have been identified. Three ${}^{24}\mathrm{Mg}\gamma$-ray lines and eight ${}^{25}\mathrm{Al}\gamma$-ray lines are observed for the first time in ${}^{25}\mathrm{Si}$ decay. The first measurement of the ${}^{25}\mathrm{Si}\beta$-delayed $\gamma$-ray intensities through the ${}^{25}\mathrm{Al}$ unbound states is reported. All the bound states of ${}^{25}\mathrm{Al}$ are observed to be populated in the $\beta$ decay of ${}^{25}\mathrm{Si}$. Several inconsistencies between the previous measurements have been resolved, and new information on the ${}^{25}\mathrm{Al}$ level scheme is provided. An enhanced decay scheme has been constructed and compared to the mirror decay of ${}^{25}\mathrm{Na}$ and the shell-model calculations.

Conclusions: The measured excitation energies, $\gamma$-ray and proton branchings, log $ft$ values, and Gamow-Teller transition strengths for the states of ${}^{25}\mathrm{Al}$ populated in the $\beta$ decay of ${}^{25}\mathrm{Si}$ are in good agreement with the shell-model calculations, offering gratifyingly consistent insights into the fine nuclear structure of ${}^{25}\mathrm{Al}$.

Figure 1

Half-life of ${}^{25}\mathrm{Si}$ measured in the present paper compared with the values previously measured by McPherson and Hardy [10], Reeder et al. [12], Hatori et al. [16], and Robertson et al. [17]. The weighed average of all published values is indicated by the solid red band.

Figure 2

$\gamma$-ray spectrum measured by the SeGA detectors magnified at (a) 1369 keV, (b) 2754 keV, (c) 2870 keV, and (d) 4238 keV. We show the raw spectrum for panel (b), (c), and (d) and the Proton-Detector-gated spectrum for panel (a) to suppress the contribution from a room background line near the 1369-keV peak. Four upper panels: The Monte Carlo (MC) simulations of the (a) 1369-keV, (b) 2754-keV, (c) 2870-keV, and (d) 4238-keV $\gamma$-ray peaks are produced by using lifetimes adopted from the data evaluation [45] and the proton energies and relative proton feeding intensities measured by Thomas et al. [18]. The black dots represent the data, the solid green lines denote the background model, and the dashed red lines denote the simulated line shapes including different contributions of proton feedings. Each proton feeding is represented by a colored line, and in the legend it is labeled with a letter $p$ followed by its center-of-mass energy. The dotted orange lines denote the small unbroadened contribution of the contaminant decay ${}^{24}\mathrm{Al}\left(\beta \gamma \right){}^{24}\mathrm{Mg}$. Four lower panels: The residual plots show the data subtracted from the simulation. Compared with a regular EMG fit of each peak, our Doppler broadening analysis substantially improved the ${\chi }_{\nu }^2$ and $p$ values, which are shown in the top-left corner of each panel.

Figure 3

${\chi }^2$ distribution of the 1368.672(5)-keV $\gamma$-ray line as a function of input $\gamma$-ray energy (black squares). A quadratic polynomial fit (solid red line) was used to determine the best-fit energy and uncertainty.

Figure 4

$\gamma$-ray spectrum (upper; black) measured by the SeGA detectors showing the assignments for the photopeaks used to construct the ${}^{25}\mathrm{Si}$ decay scheme as well as those from room background. To reduce the room background contribution, a Proton-Detector-coincident $\gamma$-ray spectrum (lower; red) is produced by requiring coincidences with particle signals from the Proton Detector. Each photopeak is labeled by the emitting nucleus and its energy rounded to the closest integer in units of keV. Peaks labeled with one or two asterisks (*) correspond to single and double escape peaks, respectively. Peaks labeled with a single dagger ($†$) are sum peaks with the summation noted. The bump at $\approx 5910$ keV is caused by the overflow of one detector with unusual gain.

Figure 5

Proton spectra measured by three central pads $\mathrm{A}+\mathrm{C}+\mathrm{D}$ (upper; blue) and central pad A (lower; red). Each proton peak from the $\beta$-delayed proton decay of ${}^{25}\mathrm{Si}$ is labeled with its center-of-mass energy rounded to the closest integer in units of keV.

Figure 6

Coincidence spectrum between the Proton Detector and SeGA detection for ${}^{25}\mathrm{Si}$ decay. The $\gamma$-ray spectrum is magnified at 4238 keV (top panel), 2754 and 2870 keV (middle panel), and 1369 keV (bottom panel), corresponding to the four $\gamma$ rays originating from the three lowest-lying ${}^{24}\mathrm{Mg}$ states.

Figure 7

Simplified decay scheme of ${}^{25}\mathrm{Si}$. The mass excesses, separation energies, $Q$ values, spins, and parities are adopted from the data evaluations [43, 45, 80]. The half-life is the weighted average of Refs. [10, 12, 16, 17] and the present paper. The $\gamma$-ray energies and the excitation energies deduced from these $\gamma$-ray energies are rounded to the nearest keV. Each $\gamma$-ray transition is denoted by a vertical arrow followed by its $\gamma$-ray energy, and the corresponding $\gamma$-ray transition intensity is denoted by the thicknesses of the arrow. Each $\beta$-decay transition is depicted by an arrow on the right side of the figure followed by its feeding intensity. The 2673- and 7902-keV ${}^{25}\mathrm{Al}$ states are observed to decay by both proton and $\gamma$-ray emissions. The newly observed 724-keV proton is emitted from the 7240-keV ${}^{25}\mathrm{Al}$ state. Each proton transition is denoted by an arrow between its initial and final states labeled alongside by its center-of-mass energy. For the sake of brevity, we omit other unbound ${}^{25}\mathrm{Al}$ states. All the energies and masses are given in units of keV. See Table 3 for details.

Figure 8

${\mathrm{\Gamma }}_p$ for the $T=3/2$ IAS in ${}^{25}\mathrm{Al}$ and its neighboring $T=1/2$ state as a function of the energy difference between the two states ($E_{x3/2}-E_{x1/2}$) calculated by the (a) USDC and (b) USDI shell models. The decay width for the state dominated by the $T=3/2$ IAS is shown by the solid red line, and decay width for the state dominated by the $T=1/2$ state is shown by the dashed black line. The solid blue band corresponds to the uncertainty of the experimental ${\mathrm{\Gamma }}_p$ value for the $T=3/2$ IAS [85, 86, 87].