Direct Capture Cross Section and the $E_p=71$ and 105 keV Resonances in the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ Reaction

The ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction, part of the neon-sodium cycle of hydrogen burning, may explain the observed anticorrelation between sodium and oxygen abundances in globular cluster stars. Its rate is controlled by a number of low-energy resonances and a slowly varying nonresonant component. Three new resonances at $E_p=156.2$, 189.5, and 259.7 keV have recently been observed and confirmed. However, significant uncertainty on the reaction rate remains due to the nonresonant process and to two suggested resonances at $E_p=71$ and 105 keV. Here, new ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ data with high statistics and low background are reported. Stringent upper limits of $6\times {10}^{-11}$ and $7\times {10}^{-11}\mathrm{eV}$ (90% confidence level), respectively, are placed on the two suggested resonances. In addition, the off-resonant $S$ factor has been measured at unprecedented low energy, constraining the contributions from a subthreshold resonance and the direct capture process. As a result, at a temperature of 0.1 GK the error bar of the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ rate is now reduced by 3 orders of magnitude.

Figure 1

Sketch of the experimental setup [28]. The ion beam entered from the right after passing through three consecutive differential pumping stages (not shown) and was stopped on the massive copper beam calorimeter with constant temperature gradient.

Figure 2

In-beam $\gamma$-ray spectra on top of the three resonances at $E_p=156.2$, 189.5, and 259.7 keV, and the rescaled background (see text). The ROI for the resonance strength determination is marked with vertical bands. The singles-sum spectra, background subtracted (bg. subtr.) and gated on add-back counts in the ROI, are also shown, together with the simulation.

Figure 3

Experimental add-back $\gamma$-ray spectra (red line), experimental background (black line, rescaled), and simulation (blue line). Runs on top of the suggested resonances at $E_p=71$ and 105 keV (left and middle panel, respectively), and for direct capture (right panel). In the right panel, the gated and background subtracted singles-sum spectrum is also included.

Figure 4

Off-resonance capture in ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ from the literature [24, 38, 40] and the present work. The result of the present fit is given by a red line with the shaded red area for the uncertainty. Top: Capture to the ground state in ${}^{23}\mathrm{Na}$. Bottom: Total $S$ factor, and Gamow peak for $T_9=0.1$.

Figure 5

Thermonuclear reaction rate for the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction from previous evaluations [10, 13] and from experiments: LUNA-HPGe [14, 15, 16, 17], TUNL [24], present work. The rates are shown relative to the frequently used [9, 42, 43] rate by Hale et al. [11]. The individual contributions from the present work are labeled. For the total rates by Hale et al. and from the present work, as well as the individual contributions from the present work, shaded error bands have been added. The contribution from the 37 keV resonance dominates at low temperature and has been omitted for clarity.