Detailed study of the decay ${}^{31}\mathrm{Cl}\left(\beta \gamma \right){}^{31}\mathrm{S}$

Background: ${}^{31}\mathrm{Cl}$ is a neutron-deficient isotope with a half-life of $T_{1/2}=190\left(1\right)$ ms. The nuclear structure of its daughter, ${}^{31}\mathrm{S}$, is important for the determination of the thermonuclear ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate, which affects the final isotopic abundances of the ejecta from classical oxygen-neon novae.

Purpose: We aim to determine the $\beta$ feedings, $\gamma$-decay branchings, and excitation energies of states populated in ${}^{31}\mathrm{S}$ and create a comprehensive decay scheme for comparison with predictions based on the shell model.

Methods: Using a ${}^{31}\mathrm{Cl}$ rare istope beam implanted into a plastic scintillator and an array of high-purity Ge detectors, $\gamma$ rays from the ${}^{31}\mathrm{Cl}\left(\beta \gamma \right){}^{31}\mathrm{S}$ decay sequence were measured. Shell-model calculations using the USDB and the recently-developed USDE interactions were performed for comparison.

Results: A ${}^{31}\mathrm{Cl} \beta$-decay scheme was constructed from the experimental data and compared to the USDB and USDE shell-model calculations based on the $\beta$ feeding and $\gamma$-decay branches of each observed state. 33 new $\gamma$-ray transitions and ten new $\beta$ decay branches were observed. The $\beta$ feeding and $\gamma$-decay branches of each observed state were compared to those from the USDB and USDE shell-model calculations. For every allowed transition predicted by the USD calculations up to an excitation energy of 6.4 MeV in ${}^{31}\mathrm{S}$, an analogous transition was found in the experimental data, enabling a one-to-one comparison with the shell model. Using these identifications, spin and parity arguments were made for observed states.

Conclusions: The new ${}^{31}\mathrm{Cl} \gamma$-decay scheme presented in this work is the most complete and precise one for this nucleus constructed to date, incorporating statistics over an order of magnitude higher than previous work on ${}^{31}\mathrm{Cl} \beta$-delayed $\gamma$ decay. Of particular interest is the discovery of a 6390-keV state that mixes with the isobaric analog state and affects the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate. Other states observed in the decay are not expected to strongly affect the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate, but the comprehensive comparison to the shell model helps to clarify spin and parity assignments of resonances that might affect the rate.

Figure 1

Particle identification plot showing ${}^{31}\mathrm{Cl}$ and strongest contaminants. Time of flight between the A1900 focal plane and the Si PIN detector is plotted on the horizontal axis while energy loss in the PIN detector is plotted on the vertical axis. The color scale denotes number of ions, with higher number of ions higher on the scale.

Figure 2

Computer-aided design drawing of the experiment setup, including the pneumatic drive attached to the PIN detectors (left inset), the central scintillator which was attached to the clover frame by a metal arm (right inset), and the full clover frame with all nine clover detectors (bottom). The liquid nitrogen dewars for the clovers are shown protruding from the clover frame, and the clover detectors themselves can be seen as the rectangular extensions into the center of the array.

Figure 3

Simple schematic showing the relative positions of the central scintillator and the surrounding germanium clover detectors (solid angle 6.8 sr). The ${}^{31}\mathrm{Cl}$ beam particles are implanted from the left into central scintillator, which detects the $\beta$ particles. The subsequent $\gamma$ rays emitted by the daughter ${}^{31}\mathrm{S}$ nucleus are detected by the surrounding clover array.

Figure 4

Upper panel: the smooth relative efficiency curve (red online) generated from fitting the relative efficiencies of the ${}^{152}\mathrm{Eu}$ and ${}^{32}\mathrm{Cl}$ data points. Lower panel: residuals of the fit in the upper panel (solid points) and the uncertainty envelope for efficiency adopted across the energy region (dashed lines).

Figure 5

Ratio of the measured photopeak integral in the scintillator-gated $\gamma$-ray spectrum to the measured integral in the ungated spectrum, the mean of the measurements (black dashed line, 80.6%) and the one-sigma envelope denoting the standard deviation of the points about that mean (dashed lines, 0.7%).

Figure 6

Cumulative Clovershare spectrum in coincidence with scintillator events showing the assignments for the photopeaks used to construct the ${}^{31}\mathrm{Cl} \beta$ decay scheme as well as those for identified contaminants. Each photopeak (black [blue online] line) is labeled by the emitting nucleus and its energy. Peaks labeled with one or two asterisks correspond to single and double escape peaks, respectively. Peaks marked with a single dagger are sum peaks with the summation noted. Peaks marked with a double dagger have multiple contributions.

Figure 7

Comprehensive ${}^{31}\mathrm{Cl}$ decay scheme produced from the analysis of the present experiment. For each level, the excitation energy rounded to the nearest keV labels the left wing of the level and its spin and parity $J^{\pi }$ are reported on the right wing. The precise excitation energies $E_x$ of each level are reported in Table 1. Each $\beta$ decay transition is depicted by a light grey (red online) arrow on the right side of the figure and includes its intensity $I_{\beta }$, also reported in Table 1. Dark grey (blue online) coloring for a level indicates that the level has not been previously observed in ${}^{31}\mathrm{Cl} \beta$ decay. $\gamma$-ray transitions between ${}^{31}\mathrm{S}$ levels are denoted in the table by the vertical arrows. Each transition is labeled by the $\gamma$-ray energy $E_{\gamma }$ and branching ratio (B.R.), which are both reported in Table 1. As with the populated levels, $\gamma$ transitions which have never been observed in ${}^{31}\mathrm{Cl} \beta$ decay before are colored grey (blue online). The scheme also incorporates the adopted branches for $\beta$-proton, $\beta -\alpha$, and unobserved $\gamma$ rays. The $*$ labeling the ground state denotes that this branch was adopted from literature.

Figure 8

Sample portions of the $\beta \gamma$ and $\beta \gamma \gamma$ coincidence spectra. The top panel shows $\beta \gamma$ transitions (black [blue online] line) from both the isobaric analog state at 6279 keV and the $3/2^{+}$ state at 6390 keV to the ground state. The middle and bottom panels also include $\beta \gamma \gamma$ transitions (grey [green online] line) from these two states to the first excited state at 1248 keV (middle panel) and the second excited state at 2234 keV (bottom panel), gated on the first and second excited states, respectively. Other ${}^{31}\mathrm{Cl}$ peaks are marked with a dot, while double escape peaks are marked with two asterisks.

Figure 9

Cumulative Clovershare $\beta \gamma$ spectrum from 7 MeV to 8 MeV in coincidence with scintillator events. The only significant peak in the spectrum, at 7049 keV, corresponds to a transition from the second $T=3/2 {}^{31}\mathrm{S}$ state to the ground state.