Searching for resonance states in ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$

Background: Globular clusters show strong correlations between different elements, such as the well-known sodium-oxygen anticorrelation. One of the main sources of uncertainty in this anticorrelation is the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rate, due to the possible influence of an unobserved resonance state at $E_x=8862$ keV ($E_{\mathrm{r},\mathrm{c}.\mathrm{m}.}=68$ keV). The influence of two higher-lying resonance states at $E_x=8894$ and 9000 keV has already been ruled out by direct ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ measurements.

Purpose: The purpose of this paper is to study excited states in ${}^{23}\mathrm{Na}$ above the proton threshold to determine if the unconfirmed resonance states in ${}^{23}\mathrm{Na}$ exist.

Methods: The nonselective proton inelastic-scattering reaction at low energies was used to search for excited states in ${}^{23}\mathrm{Na}$ above the proton threshold. Protons scattered from various targets were momentum-analyzed in the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratorium, Munich, Germany.

Results: The resonance states previously reported at $E_x=8862$, 8894, and 9000 keV in other experiments were not observed in the present experiment at any angle. This result, combined with other nonobservations of these resonance states in most other experiments, results in a strong presumption against the existence of these resonance states.

Conclusions: The previously reported resonance states at $E_x=8862$, 8894, and 9000 keV are unlikely to exist and should be omitted from future evaluations of the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rates. Indirect studies using low-energy proton inelastic scattering are a simple and yet exceptionally powerful tool in helping to constrain astrophysical reaction rates by providing nonselective information of the excited states of nuclei.

Figure 1

The focal-plane position to magnetic rigidity ($B\rho$) calibration for the data taken at a scattering angle of ${\theta }_{\mathrm{Q}3\mathrm{D}}={70}^{\circ }$. The black points correspond to the known levels in ${}^{19}\mathrm{F}$ at $E_x=8629\left(4\right)$, 8864(4), and 8953(3) keV, and in ${}^{23}\mathrm{Na}$ at $E_x=8798.7\left(8\right)$ and 8945.1(8) keV used for the calibration. Both the known uncertainties in the excitation energies listed in the ENSDF [34] and the fitting uncertainties from the peaks are included in the plot, though the error bars are frequently smaller than the points. The red line represents a best fit with a quadratic function and the blue region shows the $3\sigma$ uncertainty band.

Figure 2

(a) Excitation-energy spectrum obtained at a scattering angle of ${\theta }_{\mathrm{Q}3\mathrm{D}}={70}^{\circ }$ and assuming ${}^{23}\mathrm{Na}$ kinematics. The hollow black-lined spectrum is taken with the NaF target, and the solid red-filled spectrum is taken with the LiF target. The solid black vertical lines show the listed energies of levels in ${}^{23}\mathrm{Na}$ from the ENSDF [34] with the associated gray box showing the listed $E_x$ uncertainty and a blue box showing the $E_x$ uncertainty from the present measurement. The green dotted vertical lines show the energies of the tentative resonances at $E_x=8862$, 8894, and 9000 keV from Ref. [27]. The center-of-mass energy for the ${}^{22}\mathrm{Ne}+p$ colliding system is shown on the top axis. (b) The corresponding $1\sigma$, $2\sigma$, and $3\sigma$ uncertainty bands for the excitation-energy calibration relative to the central value for the ${70}^{\circ }$ data.

Figure 3

Same as Fig. 2 at ${\theta }_{\mathrm{Q}3\mathrm{D}}={50}^{\circ }$ except that the red-filled spectrum is taken with the carbon target; the peak in the spectrum is from a contaminating ${}^{16}\mathrm{O}$ state, likely from water or oil on the carbon and NaF targets (or the carbon backing of the NaF target). The spectrum was calibrated using the ${}^{23}\mathrm{Na}$ states at $E_x=8798.7\left(8\right)$, 8975.3(7), and 9072(3) keV and the ${}^{16}\mathrm{O}$ state at $E_x=8871.9\left(5\right)$ keV, which is the only peak in the red-filled spectrum with the carbon target. The peak at around $E_x=8900$ keV is an unidentified contaminant since it does not appear at other angles and is broader than the spectrometer resolution, which may be due to the state itself being broad or the kinematics being out of focus.

Figure 4

Same as Fig. 3 at ${\theta }_{\mathrm{Q}3\mathrm{D}}={40}^{\circ }$. The spectrum was calibrated using the ${}^{23}\mathrm{Na}$ states at $E_x=8798.7\left(8\right)$, 9072(3), and 9113(3) keV; the ${}^{19}\mathrm{F}$ state at $E_x=8864\left(4\right)$ keV; and the ${}^{16}\mathrm{O}$ state at $E_x=8871.9\left(5\right)$ keV.

Figure 5

Same as Fig. 3 at ${\theta }_{\mathrm{Q}3\mathrm{D}}={35}^{\circ }$. The ${}^{23}\mathrm{Na}$ states at $E_x=8798.7\left(8\right)$ and 9113(3) keV, the ${}^{19}\mathrm{F}$ state at $E_x=8864\left(4\right)$ keV, and the ${}^{16}\mathrm{O}$ state at $E_x=8871.9\left(5\right)$ keV were used to calibrate at this angle.

Figure 6

Same as Fig. 3 but for ${\theta }_{\mathrm{Q}3\mathrm{D}}={25}^{\circ }$. The ${}^{23}\mathrm{Na}$ states at $E_x=8798.7\left(8\right)$, 8975.3(7), and 9113(3) keV and the ${}^{19}\mathrm{F}$ state at $E_x=8864\left(4\right)$ keV were used to calibrate at this angle.