Direct measurement of resonance strengths in ${}^{34}\mathrm{S}(\alpha ,\gamma ){}^{38}\mathrm{Ar}$ at astrophysically relevant energies using the DRAGON recoil separator

Background: Nucleosynthesis of mid-mass elements is thought to occur under hot and explosive astrophysical conditions. Radiative $\alpha$ capture on ${}^{34}\mathrm{S}$ has been shown to impact nucleosynthesis in several such conditions, including core and shell oxygen burning, explosive oxygen burning, and type Ia supernovae.

Purpose: Broad uncertainties exist in the literature for the strengths of three resonances within the astrophysically relevant energy range ($E_{\text{CM}}=1.94–3.42\mathrm{MeV}$ at $T=2.2\mathrm{GK}$). Further, there are several states in ${}^{38}\mathrm{Ar}$ within this energy range which have not been previously measured. This work aimed to remeasure the resonance strengths of states for which broad uncertainty existed as well as to measure the resonance strengths and energies of previously unmeasured states.

Methods: Resonance strengths and energies of eight narrow resonances (five of which had not been previously studied) were measured in inverse kinematics with the DRAGON facility at TRIUMF by impinging an isotopically pure beam of ${}^{34}\mathrm{S}$ ions on a windowless ${}^4\mathrm{He}$ gas target. Prompt $\gamma$ emissions of de-exciting ${}^{38}\mathrm{Ar}$ recoils were detected in an array of bismuth germanate scintillators in coincidence with recoil nuclei, which were separated from unreacted beam ions by an electromagnetic mass separator and detected by a time-of-flight system and a multianode ionization chamber.

Results: The present measurements agree with previous results. Broad uncertainty in the resonance strength of the $E_{\text{CM}}=2709\mathrm{keV}$ resonance persists. Resonance strengths and energies were determined for five low-energy resonances which had not been studied previously, and their strengths were determined to be significantly weaker than those of previously measured resonances.

Conclusions: The five previously unmeasured resonances were found not to contribute significantly to the total thermonuclear reaction rate. A median total thermonuclear reaction rate calculated using data from the present work along with existing literature values using the STARLIB rate calculator agrees with the NON-SMOKER statistical model calculation as well as the REACLIB and STARLIB library rates at explosive and nonexplosive oxygen-burning temperatures ($T=3–4\mathrm{GK}$ and $T=1.5–2.7\mathrm{GK}$, respectively).

Figure 1

Partial level diagram of ${}^{38}\mathrm{Ar}$. States in blue were measured in this work. The two states in red (also measured in this work) are those for which there exists broad uncertainty in the literature values for the resonance strengths. Excitation energies are those reported in Ref. [16]. The astrophysically relevant energy range for oxygen burning (calculated from Ref. [7]) is illustrated on the right.

Figure 2

Schematic of the DRAGON recoil mass separator.

Figure 3

BGO $\gamma$-ray array energy spectrum of highest energy $\gamma$ per event for the 2389-keV resonance (blue) compared to geant-3 simulation (red).

Figure 4

(a) Overlay of ionizaiton chamber spectra displaying the response of the first two anodes to attenuated ${}^{34}\mathrm{S}$ beam (grey circles), singles IC events (blue squares) and $\gamma -$ heavy ion coincidences subjected to gates on the separator TOF and MCP TOF (red triangles - see text for detailed explanation). (b) Projection of panel (a) onto the anode[0] = anode[1] axis allowing for a double Gaussian fit to extract recoil statistics. Vertical lines indicate the selected signal region.

Figure 5

Beam normalization coefficients $R$ for all runs during the yield measurement of the $E_{\text{CM}}=2166\mathrm{keV}$ resonance. The solid horizontal line is the value of $\overline{R}$ obtained from a ${\chi }^2$ fit to the data. Dashed horizontal lines are the statistical uncertainty in $\overline{R}$, and dotted horizontal lines are the total (statistical and systematic added in quadrature) uncertainty in $\overline{R}$.

Figure 6

Comparison of stopping power of ${}^{34}\mathrm{S}$ in ${}^4\mathrm{He}$ to SRIM 2013 calculation. The dashed line represents the SRIM 2013 calculation scaled by a factor of 0.9.

Figure 7

CSD measurements of ${}^{40}\mathrm{Ar}$ passing through ${}^4\mathrm{He}$ gas at a laboratory-frame bombarding energy of $E_{\text{b}}^{\text{lab}}=21.58\mathrm{MeV}$. The black and dashed gray curves are the average equilibrium CSDs predicted by the semi-empirical formulas of Refs. [35, 36], respectively.

Figure 8

BGO $z$-position spectrum of the highest energy $\gamma$-ray per event for (coincident) events passing all recoil cuts for the 2388-keV resonance measurement.

Figure 9

Resonance strength vs CM energy from the present work (singles and coincidence) compared with literature values [9, 10]. Gray bars indicate the energy thickness (55–75 keV in the CM system) of the gas target during the yield measurement. Statistical and systematic uncertainties are displayed combined in quadrature.

Figure 10

Top panel: Median total thermonuclear reaction rate and associated $1-\sigma$ quantiles (blue dashed lines) calculated using the values in Table 4 as input for the STARLIB rate calculator [38]. Bottom panel: NON-SMOKER [40], REACLIB [41], and STARLIB [38] rates normalized to the median total rate calculated in the present work. The STARLIB rate is calculated from the talys [42, 43] code and is plotted with its recommended factor uncertainty (orange dash-double-dotted lines). See text for details.

Figure 11

Top panel: Resonant reaction rates calculated from the results of the present work compared to the median total rate calculated in the present work and the total resonant reaction rate calculated from Eq. (8) using the values in Table 4. Bottom panel: Resonant rates normalized to the median total rate calculated in the present work.