Developing the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}^{*}\left(p\right)\left(\gamma \right)$ reaction to probe the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate in classical novae

Background: The ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate is one of the largest remaining sources of uncertainty in the final abundances of nuclei created in a classical nova involving a ONe white dwarf. The reaction rate directly influences silicon isotopic ratios, which are used as identifiers of presolar grains with nova origins. In addition, the uncertainty in the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate has been found to limit the use of nova nuclear thermometers based on observations of elemental ratios in nova ejecta.

Purpose: Reduce uncertainties in the nuclear data for proton-unbound states in ${}^{31}\mathrm{S}$, which act as resonances for the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction at classical nova temperatures, and develop a technique for high efficiency, high-resolution reaction-decay coincidence measurements.

Methods: The ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction was used to populate the states of interest in ${}^{31}\mathrm{S}$. The experiment was performed at the Texas A&M Cyclotron Institute using the LLNL Hyperion array for the detection of charged particles and $\gamma$ rays. A downstream silicon telescope was used to select reaction deuterons, and a single upstream silicon detector was used to measure protons emitted in the decay of unbound ${}^{31}\mathrm{S}$ levels.

Results: Several states in ${}^{31}\mathrm{S}$ above the proton separation energy were observed to have been populated. Decay protons from the resonant states in ${}^{31}\mathrm{S}$ were identified as events in the upstream silicon detectors that came in coincidence with deuterons in the downstream telescope. Protons emitted from these states were measured and branching ratios extracted.

Conclusions: While no new reaction rate is derived, spin-parity assignments for several higher-lying proton unbound states have been confirmed. Measured $p_0$ branching ratios for these levels have been compared to previous measurements with good agreement, and in some cases provided a reduction in uncertainty. The previously identified $T=3/2$ state may have been incorrectly assigned a large $p_0$ branching ratio in a previous measurement. The technique of measuring reaction-decay coincidences with a particle-gamma setup appears promising.

Figure 1

The region of the nuclear chart around ${}^{30}\mathrm{P}$ with some of the reactions important for ONe nova nucleosynthesis labeled. The values displayed above the blue diagonal lines are the ${\beta }^{+}$-decay half lives. Figure reproduced from Ref. [3].

Figure 2

The sensitivity of ${}^{30}\mathrm{Si}$ abundance to the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate for different peak ONe nova temperatures. The dashed lines correspond to the reaction rate derived from the Hauser-Feshbach (HF) statistical method and the resulting ${}^{30}\mathrm{Si}$ abundance. The data presented here have been extracted from Tables 5, 6, 7, and 8 in Ref. [8].

Figure 3

An example of a $\mathrm{\Delta }\mathrm{E}$-E particle identification plot. The data shown here are for a scattering angle of ${20}^{\circ }$ and were taken over one hour. Scattered protons, deuterons, tritons, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$, produced in the corresponding proton-induced reactions on nuclei in the target, are visible and well separated. The intensity, ranging from single counts (blue/dark grey) to thousands of counts (yellow/light grey) per bin, has not been normalized.

Figure 4

Gamma-ray detection efficiency curve. Fits for source data only (blue/light grey outer band) and source data plus in-beam data (red/dark grey inner band) are shown, with the corresponding uncertainties. Including both source and in-beam data allows for more accurate extrapolation to higher gamma-ray energies.

Figure 5

Deuteron singles spectrum corrected for the the kinematics of the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction. The black histogram is the spectrum observed from the ZnS target. The ground-state peak resolution is on the order of 150 keV. The blue and red histograms are the spectra observed from the mylar and zinc foils respectively, which have been normalized to the sulfur spectrum for visual clarity. Background runs on a carbon foil were also taken, but are not shown here as the peaks arising from reactions on carbon are already apparent in the mylar target data.

Figure 6

Deuteron angular distributions for the (a) 6872(6)-keV, (b) 7036(7)-keV, and (c) 7171(8)-keV states. The data from this measurement are shown as black circles. For the 7036(7)-keV state, two previous measurements reported deuteron angular distributions (Kozub et al. [13] and Ma et al. [14]) and these data are shown along side the present work. The different color curves represent DWBA calculations with different amounts of transferred angular momentum. The calculations were performed using TWOFNR [23] with the optical model parameters found in Table 2.

Figure 7

Proton decay matrix for the emission of protons from excited states in ${}^{31}\mathrm{S}$. The excitation energy of the final state in ${}^{30}\mathrm{P}$ is shown vs the excitation energy of the initial state in ${}^{31}\mathrm{S}$. Horizontal red dotted lines are drawn at the known excitation energies of low-lying states in ${}^{30}\mathrm{P}$. The low-level background is due to random coincidences within the data acquisition coincidence timing window. Intensity scale (blue/dark grey to yellow/light grey) displays raw counts.

Figure 8

The deuteron singles spectrum (black) is compared with the deuteron-proton coincidence spectra for the $p_0$ (blue, lowest energy threshold), $p_{1,2}$ (red), $p_3$ (green), and $p_4$ (purple, highest energy threshold) proton-decay branches. All of the deuteron-proton coincidence spectra have been scaled up by a factor of 10 for visual comparison with the singles spectrum. The correspondingly-labeled dashed lines indicate the threshold for that decay channel.

Figure 9

Deuteron-proton angular correlations for the six cleanly observed $p_0$ decay branches, increasing in excitation energy from panels (a) through (f). The angular correlations, in number of decays per steradian normalized to the number of times the resonance was formed, are plotted as a function of the center of mass angle of the decay. The red-dotted lines correspond to best fit to the data using Eq. (2).

Figure 10

Deuteron-gated, doppler-corrected gamma spectrum showing the 6254.4(16) keV direct to ground-state transition, as well as peaks arising from the contaminant ${}^{12}\mathrm{C}$(p,$\mathrm{d}){}^{11}\mathrm{C}$ reaction. The deuteron gate was set to energies corresponding to ${}^{31}\mathrm{S}$ excitation energies between 6150 and 6350 keV.