First measurement of ${}^{30}\mathrm{S}+\alpha$ resonant elastic scattering for the ${}^{30}\mathrm{S}(\alpha ,p)$ reaction rate

Background: Type I x-ray bursts are the most frequently observed thermonuclear explosions in the galaxy, resulting from thermonuclear runaway on the surface of an accreting neutron star. The ${}^{30}\mathrm{S}(\alpha ,p)$ reaction plays a critical role in burst models, yet insufficient experimental information is available to calculate a reliable, precise rate for this reaction.

Purpose: Our measurement was conducted to search for states in ${}^{34}\mathrm{Ar}$ and determine their quantum properties. In particular, natural-parity states with large $\alpha$-decay partial widths should dominate the stellar reaction rate.

Method: We performed the first measurement of ${}^{30}\mathrm{S}+\alpha$ resonant elastic scattering up to a center-of-mass energy of 5.5 MeV using a radioactive ion beam. The experiment utilized a thick gaseous active target system and silicon detector array in inverse kinematics.

Results: We obtained an excitation function for ${}^{30}\mathrm{S}(\alpha ,\alpha )$ near ${150}^{\circ }$ in the center-of-mass frame. The experimental data were analyzed with $R$-matrix calculations, and we observed three new resonant patterns between 11.1 and 12.1 MeV, extracting their properties of resonance energy, widths, spin, and parity.

Conclusions: We calculated the resonant thermonuclear reaction rate of ${}^{30}\mathrm{S}(\alpha ,p)$ based on all available experimental data of ${}^{34}\mathrm{Ar}$ and found an upper limit about one order of magnitude larger than a rate determined using a statistical model. The astrophysical impact of these two rates has been investigated through one-zone postprocessing type I x-ray burst calculations. We find that our new upper limit for the ${}^{30}\mathrm{S}(\alpha ,p){}^{33}\mathrm{Cl}$ rate significantly affects the predicted nuclear energy generation rate during the burst.

Figure 1

Schematic of the experimental setup, consisting of two parallel plate avalanche counters (PPACs), the active target, and silicon telescope arrays. Note that between PPACb and the active target, the beam impinges on an entrance window, which retains the active target fill gas. The beam is tracked in the central low-gain region (“active target region,” 20 cm), surrounded on three sides by high-gain regions and silicon telescopes to measure outgoing light ions (right side telescope not depicted). Beneath each gas electron multiplier (GEM) is a readout pattern, separated into 4 mm thick backgammon pads. $\mathrm{\Delta }E$ is simply proportional to the charge collected by each pad. The coordinate system is one where the beam axis defines positive $Z$, the rest following left-handed conventions. $Z$ and $X$ positions are determined by the pad number and comparing charge collection on either side of the backgammon, respectively. The $Y$ position is determined by the electron drift time.

Figure 2

Top-down cartoon of the experimental setup and the detectors used in the data analysis (not to scale—PPACs in particular are much further from the active target chamber than depicted). The differences between a higher energy scattering (denoted “${\alpha }_1$”) and a lower energy scattering (“${\alpha }_2$”) are shown.

Figure 3

Calibrated Bragg curve of the unscattered ${}^{30}\mathrm{S}$ beam over the low-gain region of the active target. The depth of each pad is 4 mm with the beam penetration depth correlated with the pad number. Data from several pads are not shown for a variety of reasons; in general it was either because the electronics did not record a signal, or the energy deposit was arbitrarily lower than expected.

Figure 4

Timing from rf vs PPACa $X$ position for the unscattered beam, showing gates for ${}^{30}\mathrm{S}$ and ${}^{29}\mathrm{P}$. The rf signal is recorded with PPACa as the start and the cyclotron radio-frequency signal as the stop, and thus it represents a relative flight time between ions in the cocktail beam.

Figure 5

$\mathrm{\Delta }E-E$ plot for light ion particle identification during the ${}^{30}\mathrm{S}+\alpha$ scattering measurement. The long-dashed black line, short-dashed grey line, and solid (red) line show calculations for $\alpha$ particles, deuterons, and protons, respectively, using the experimental conditions.

Figure 6

Energy spectrum of scattered $\alpha$ particles gating on the ${}^{30}\mathrm{S}$ RIB determined by the kinematic solution. As the high-gain GEM and SSD must both be hit for an event to register, it is only a portion of the total events which are analyzed. Hints of some resonant structure can be seen around 4500 and 5000 keV. The data cut off at low energy as the scattered $\alpha$ particles do not have enough energy to reach the SSD and are instead stopped in the gas.

Figure 7

Residual light ion energy as measured by the SSD in channels on the abscissa against the system ToF in nanoseconds on the ordinate. Significant $\alpha$ background is seen around channel 1000 in the SSD energy. The locus of true elastic scattering events selected by the kinematic solution fall within the depicted gate; however, it can be observed that one locus of the beamlike $\alpha$ particles overlaps with the region of the true events. See the text.

Figure 8

Uncertainty in determination of the center-of-mass energy $E_{\mathrm{c}.\mathrm{m}.}$ in MeV (solid line) and average scattering angle ${\vartheta }_{\mathrm{c}.\mathrm{m}.}$ in degrees (dashed line) as functions of the center-of-mass energy in keV. The range of angles measured in the laboratory frame is roughly ${10}^{\circ }\le {\vartheta }_{\mathrm{lab}}\le {20}^{\circ }$ as $2{\vartheta }_{\mathrm{lab}}+{\vartheta }_{\mathrm{c}.\mathrm{m}.}={180}^{\circ }$.

Figure 9

${}^{30}\mathrm{S}+\alpha$ elastic scattering excitation function including fits. (a) The energy range displayed is the entire set of continuous data in the raw excitation function, except at the lower energy side where the plot is terminated at the point where all the $\alpha$ particles can no longer reach the detector from stopping in the fill gas. The bumps observed around 3.5 MeV correspond to a region of large $\alpha$ background, as depicted in Fig. 7. Three resonancelike structures are seen at $4.0\text{MeV}<E_{\mathrm{c}.\mathrm{m}.}<5.5$ MeV. The data are fit with a multichannel ($\alpha$ and $p$), multilevel $R$-matrix formalism, and the results for a selected combination of ${\ell }_{\alpha }$ transfers are shown (though all combinations up to ${\ell }_{\alpha }\le 4$ were tested, and ${\ell }_{\alpha }=5,6$ never gave good fits). The adopted parameters of these three newly discovered resonances are shown in Table 2. (b) All physically allowed ${\ell }_{\alpha }$ values for the $E_{\mathrm{r}}=4.78$ MeV resonance, showing the unambiguous assignment of $\ell =2$. See the text.

Figure 10

Relative dependence of the resonance strength $\omega \gamma$ from individual states based on their spin $J$ under the assumption that $\gamma \approx {\mathrm{\Gamma }}_{\alpha }\propto W_{{\mathrm{\Gamma }}_{\alpha }}$. The resonance strengths are normalized to the case of $J=0$, denoted as ${\omega }_0{\gamma }_0$. The $E_{\mathrm{r}}=2.25$-MeV state is the closest to the center of the 1.3-GK Gamow window.

Figure 11

Calculations of the ${}^{30}\mathrm{S}(\alpha ,p)$ stellar reaction rate from 1–10 GK. The statistical model (SM) rate from non-smoker [67] is shown as the long-dashed black line, to which all the rates are normalized. The dashed grey lines represent our new higher-energy resonances observed at CRIB with our best fit quantum properties. The dotted (blue) lines represent the 13 resonances from the ${}^{36}\mathrm{Ar}(p,t)$ RCNP experiment [31], where we made a couple of assumptions about their quantum properties. The sum of these individual resonant contributions is shown as the thick solid (red) line. The adopted individual resonance properties are listed in Table 3.

Figure 12

Nuclear energy generation rates during one-zone XRB calculations using the K04 thermodynamic history [13]. Results using the present rate (black line) and a statistical model rate [67] (grey line) are indicated.