Toward complete spectroscopy using $\beta$ decay: The example of ${}^{32}\mathrm{Cl}\left(\beta \gamma \right){}^{32}\mathrm{S}$

Background: ${}^{32}\mathrm{Cl}$ is a neutron-deficient isotope with a $\beta$-decay half-life of 298 ms and a spin and parity of $J^{\pi }=1^{+}$. Previous measurements of ${}^{32}\mathrm{Cl} \beta$-delayed $\gamma$ rays have yielded a $\beta$-decay scheme with twelve $\beta$-decay transitions, contributing to studies of nuclear structure and fundamental symmetries. Those experiments have been limited to the observation of ${}^{32}\mathrm{S}$ states with $J^{\pi }=0^{+},1^{+},2^{+}$.

Purpose: Our goal is to search for new $\beta$-delayed $\gamma$ rays and $\beta$-decay transitions of ${}^{32}\mathrm{Cl}$ to ${}^{32}\mathrm{S}$.

Methods: A measurement of ${}^{32}\mathrm{Cl} \beta$-delayed $\gamma$ decay has been performed using the Clovershare array of high-purity germanium detectors at the National Superconducting Cyclotron Laboratory.

Results: By acquiring the highest-statistics ${}^{32}\mathrm{Cl} \beta$-delayed $\gamma$-ray spectrum to date and exploiting a new sensitivity to $\gamma -\gamma$ coincidences, this experiment has enabled the observation of nine previously unobserved $\beta$-delayed $\gamma$-ray transitions, leading to the inference of five $\beta$-decay transitions never before observed in ${}^{32}\mathrm{Cl} \beta$-delayed $\gamma$ decay. The set of observed states includes negative-parity states for the first time. By combining the new information with data from previous work, the lifetimes and partial widths of the 8861- and 9650-keV states of ${}^{32}\mathrm{S}$ have been determined. In addition, the ${}^{31}\mathrm{P}(p,\alpha ){}^{28}\mathrm{Si}$ resonance strength of the 9650-keV state has been limited to $\omega \gamma <9.8$ meV, which is an improvement over direct measurements.

Conclusion: An enhanced decay scheme has been constructed. Most of the excited bound ${}^{32}\mathrm{S}$ states that would correspond to allowed and first-forbidden $\beta$-decay transitions have been observed, demonstrating the potential of $\beta$-decay experiments to approach complete spectroscopy measurements at the next generation of radioactive beam facilities. The observed positive-parity levels are well matched by $sd$ shell-model calculations.

Figure 1

Mechanical design drawing of the experimental apparatus used in the present work. The ${}^{32}\mathrm{Cl}$ beam enters from the left and is implanted into the scintillator (obscured) in the center of the Ge array. The $\beta$-delayed $\gamma$ rays are detected by the nine surrounding high-purity Ge detectors, with eight detectors forming two rings around the scintillator and one detector along the beam axis. Each of the nine high-purity Ge detectors consists of four crystals.

Figure 2

${}^{32}\mathrm{Cl} \beta$-delayed $\gamma$-decay spectrum gated on scintillator events. ${}^{32}\mathrm{S}$ peaks are labeled by $\gamma$-ray energy over the range of $E_{\gamma }=0–4250$ keV. A single asterisk represents a first-escape peak and a double asterisk represents a second escape peak.

Figure 3

Same as Fig. 2 for the $\gamma$-ray energy range of $E_{\gamma }=4100–8250$ keV

Figure 4

Nine segments of the histogram in Figs. 2 and 3 displaying the peaks corresponding to the previously unobserved $\gamma$ rays presented in this analysis (blue online) and the corresponding fits (red online). (a) The 1659-keV photopeak, which corresponds to decays from the $2^{+}$ state at 6666 keV to the $3^{-}$ state at 5006 keV. (b) The 2775-keV photopeak, which corresponds to decays from the $3^{-}$ state at 5006 keV. (c) The 5798-keV photopeak. (d) The 7484-keV photopeak. (e) The 8125-keV photopeak. (f) The first-escape peak at 7895 keV that was used, following the procedure described in Sec. 3b3, to determine the intensity of the 8407-keV photopeak. (g) The second escape peak at 7839 keV that was used to determine the intensity of the 8861-keV photopeak. (h) The second escape peak at 8186 keV that was used to determine the intensity of the 9207-keV photopeak. (i) Both the 4954-keV and 4959-keV photopeaks. The 4954-keV photopeak is newly observed, while the 4959-keV photopeak was observed in previous experiments.

Figure 5

Systematic uncertainty envelope for the determination of $\gamma$-ray energies constructed from the calibration standards adopted from [15].

Figure 6

(a) Relative $\gamma$-ray efficiency curve for the Clovershare array. (b) Residuals between the plotted functional form of the efficiency curve and the data points. The error envelope of the relative efficiencies is plotted, as a dashed line, on the residual plot.

Figure 7

(a) Ratio of the second escape peak integral value (EP) to the photopeak integral value (PP). The plot was fit with a linear function, (${\chi }^2/\nu =0.18$). (b) Residuals of the linear fit.

Figure 8

${}^{32}\mathrm{Cl} \beta$-delayed $\gamma$-decay scheme derived from the present work. Energy levels and transitions shown in gray represent previously known states and decays. Energy levels and transitions shown in black represent states and decays observed in the present work for the first time from the $\beta$ decay of ${}^{32}\mathrm{Cl}$. The $\beta$-decay feeding values are shown to the right of the ${}^{32}\mathrm{S}$ energy states. $\beta$-decay intensities are shown in percent of ${}^{32}\mathrm{Cl}$ decays, $\gamma$-decay probabilities are shown in percent of $\gamma$ decays from the respective state, and their values and uncertainties can be found in Table 4. The $\beta$ transition labeled with $†$ was adopted from Armini et al. [13] and the ones labeled with $♮$ include $\beta -\alpha , \beta -p$, and $\beta -\gamma$ branches from ENSDF [8]. The energy levels are not plotted to scale, but simply increasing incrementally.

Figure 9

The $\beta -\gamma -\gamma$ coincidence spectrum for the 2230-keV gate. The darker (blue online) histogram is the coincidence spectrum and the lighter (green online) histogram was obtained by gating on the background in the $\gamma$-ray energy spectrum near the 2230-keV peak. The labeled peaks correspond to ${}^{32}\mathrm{S}\gamma$-ray transitions found to be in coincidence with the 2230-keV $\gamma$-ray. The single asterisk represents a first-escape peak.

Figure 10

Comparison of experimental and theoretical summed Gamow Teller strengths for the $\beta$ decay of ${}^{32}\mathrm{Cl}$ to ${}^{32}\mathrm{S}$ states. The gray solid line represents the USDB theoretical values and the black solid line represents the experimental values with the corresponding uncertainties represented by black dashed lines. Due to the unknown mixing ratio, the $B\left(\text{GT}\right)$ value for the transition to the IAS was assumed to be zero and the transition to the 7190-keV state was assumed to be purely Gamow-Teller. The $B\left(\text{GT}\right)$ value for the transition to the ground state was calculated from the $ft$ value adopted from [13].