Experimental study of ${}^{35}\mathrm{Cl}$ excited states via ${}^{32}\mathrm{S}(\alpha ,p)$

Background: The presolar grains originating in oxygen-neon novae may be identified more easily than those of other stellar sources if their sulfur isotopic ratios (${}^{33}\mathrm{S}/{}^{32}\mathrm{S}$ and ${}^{34}\mathrm{S}/{}^{32}\mathrm{S}$) are compared with the theoretical ones. The accuracy of such a comparison depends on reliable ${}^{33}\mathrm{S}(p,\gamma ){}^{34}\mathrm{Cl}$ and ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ reaction rates at the nova temperature regime. The latter rate has recently been computed based on experimental input, and many new excited states in ${}^{35}\mathrm{Cl}$ were discovered above the proton threshold. As a result, the experimental ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ rate was found to be less uncertain and 2–5 times smaller than the theoretical one. Consequently, the simulated ${}^{34}\mathrm{S}/{}^{32}\mathrm{S}$ isotopic ratio for nova presolar grains was predicted to be smaller than that of type II supernova grains by a factor of 1.5 to 3.7.

Purpose: The present study was performed to confirm the existence of these new resonances, and to improve the remaining uncertainties in the ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ reaction rate.

Methods: Energies and spin-parities of the ${}^{35}\mathrm{Cl}$ excited levels were investigated via high-resolution charged-particle spectroscopy with an Enge split-pole spectrograph using the ${}^{32}\mathrm{S}(\alpha ,p){}^{35}\mathrm{Cl}$ reaction. Differential cross sections of the outgoing protons were measured at $E_{\alpha }=21$ MeV. Distorted-wave Born approximation calculations were carried out to constrain the spin-parity assignments of observed levels, with special attention to those significant in determination of the ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ reaction rate over the nova temperature regime.

Results: The existence of these newly discovered states are largely confirmed, although a few states were not observed in this study. The spins and parities of a few ${}^{35}\mathrm{Cl}$ states were assigned tentatively for the first time.

Conclusions: The present ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ experimental thermonuclear reaction rate at 0.1–0.4 GK is consistent within $1\sigma$ with the previous evaluation. However, our rate uncertainty is larger than before due to a more realistic treatment of the uncertainties in the rate input. In comparison with the previous rate evaluation, where the high and low rates differed by less than a factor of 2 over the nova temperature regime, the ratio of the present limit rates is at most a factor of 3.5 at 0.12 GK. At temperatures above 0.2 GK, we recommend the future work to focus on determination of the unknown properties of four excited states of ${}^{35}\mathrm{Cl}$: 6643, 6761, 6780, and 6800 keV.

Figure 1

Spectra from the ${}^{32}\mathrm{S}(\alpha ,p){}^{35}\mathrm{Cl}$ reaction at ${\theta }_{\mathrm{lab}}={15}^{\circ }$ (a), ${40}^{\circ }$ (b), and ${30}^{\circ }$ (zoomed in on the region of interest) (c). The spectra at ${15}^{\circ }$ and ${30}^{\circ }$ are obtained using the CdS target, and the one at ${40}^{\circ }$ is obtained using the ${\mathrm{Sb}}_2{\mathrm{S}}_3$ target. The ${40}^{\circ }$ spectrum is shifted back to compensate for the kinematics shift due to a change in the scattering angle. Therefore, the peaks in panels (a) and (b) are lined up with each other. Peaks corresponding to ${}^{35}\mathrm{Cl}$ states are labeled with energies (in keV) from the present work except those denoted by asterisks, which were used as internal calibration using energies from Ref. [18]. For clarity, not all peaks are labeled. The main contaminant peaks are from the ground states (g.s.) of ${}^{15}\mathrm{N}$ and ${}^4\mathrm{He}$ from the ${}^{12}\mathrm{C}(\alpha ,p)$ and ${}^1\mathrm{H}(\alpha ,p)$ reactions, respectively. The ${}^4\mathrm{He}\left(\text{g.s.}\right)$ is significantly out of focus and broad due to the substantial differences in the kinematics of the ${}^1\mathrm{H}(\alpha ,p)$ and ${}^{32}\mathrm{S}(\alpha ,p)$ reactions.

Figure 2

Spectrum from the ${}^{28}\mathrm{Si}(\alpha ,p){}^{31}\mathrm{P}$ calibration reaction measured using the ${\mathrm{SiO}}_2$ target at ${\theta }_{\mathrm{lab}}={15}^{\circ }$. Peaks corresponding to ${}^{31}\mathrm{P}$ states are labeled with energies (in keV, rounded to the nearest integer) from the present work. Those labeled by an asterisk are used as calibration energies in our initial calibration fits; they are adopted from Ref. [24]. The main contaminant peaks are from the ${}^1\mathrm{H}(\alpha ,p){}^4\mathrm{He}$, ${}^{12}\mathrm{C}(\alpha ,p){}^{15}\mathrm{N}$, and ${}^{16}\mathrm{O}(\alpha ,p){}^{19}\mathrm{F}$ reactions and are labeled with their parent nuclei and their energies (in MeV). g.s. indicates ground state.

Figure 3

The momentum spectrum of $\alpha$ particles elastically scattered off of the CdS target at ${30}^{\circ }$. The spectrum is obtained using the TUNL Enge split-pole spectrograph and its focal plane detector package. The small shoulder labeled by S refers to other stable isotopes of sulfur in the CdS target. The negligible nitrogen contamination does not show up on the RBS spectra and may be coming from vacuum contamination of the target chamber. No excited states produced from $(\alpha ,p)$ reactions on the nitrogen or ${}^{13}\mathrm{C}$ contamination of the CdS target were observed in the ${}^{32}\mathrm{S}(\alpha ,p)$ spectra. Due to kinematic broadening [23, 33, 34, 35], only the $\alpha$ particles scattered off of ${}^{32}\mathrm{S}$ are in focus.

Figure 4

The filled circles represent the angular distribution of the ratio of the center-of-mass differential to Rutherford ${}^4\mathrm{He}+{}^{32}\mathrm{S}$ elastic scattering cross section at 21 MeV. If not shown, the error bar is smaller than the point size. The curves are the theoretical DWBA calculations using fresco [28]. Each curve is computed via optimizing the parameters of a specific global optical potential model taken from Refs. [29, 30] and the ${}^4\mathrm{He}+{}^{32}\mathrm{S}$ potential of Ref. [31] (see p. 83). The latter was obtained at 23.8 MeV. The global Su-2015 [30] optimized models describe the data the best.

Figure 5

Center-of-mass proton angular distributions of the ${}^{32}\mathrm{S}(\alpha ,p)$ reaction at 21 MeV (filled circles) compared with the DWBA curves (see legends) calculated using fresco [28]. If not shown, the error bar is smaller than the point size. The excited energies (in keV, rounded to the nearest integer) are given on the top of each panel.

Figure 6

Similar to Fig. 5, at additional excitation energies.

Figure 7

Similar to Fig. 5, at additional excitation energies.

Figure 8

Rate uncertainties for the ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ reaction calculated using the resonance parameters presented in Table 3. The rates are normalized to the recommended rate so the recommended rate is at unity. The thick and thin solid lines correspond to the $1\sigma$ and $2\sigma$ uncertainty bands, respectively, with the color scale highlighting the continuous reaction rate probability distribution. The green (grey in print version) lines correspond to the “high” and “low” reaction rates presented by Ref. [16].

Figure 9

Resonance contributions to the total reaction rate. Each color band signifies a single narrow resonance and its contribution to the reaction rate. A finite thickness to these lines denotes those resonances which may contribute significantly to the rate, or may only contribute in a minor way. For example, all three resonances at $E_r^{\mathrm{c}.\mathrm{m}.}=390$, 409, and 429 keV are not known well enough to determine which dominates the reaction rate at 250 MK. The dotted line represents the aggregate contribution of higher lying resonances not significant for the nova temperature regime.