Searching for resonance states in $^{22}$Ne($p,γ$)$^{23}$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 $^{22}$Ne($p,γ$)$^{23}$Na reaction rate, due to the possible influence of an unobserved resonance state at $E_\mathrm{x} = 8862$ keV ($E_\mathrm{r, c.m.} = 68$ keV). The influence of two higher-lying resonance states at $E_\mathrm{x} = 8894$ and $9000$ keV has already been ruled out by direct $^{22}$Ne($p,γ$)$^{23}$Na measurementsPurpose: To study excited states in $^{23}$Na above the proton threshold to determine if the unconfirmed resonance states in $^{23}$Na exist. Methods: The non-selective proton inelastic scattering reaction at low energies was used to search for excited states in $^{23}$Na above the proton threshold. Protons scattered from various targets were momentum-analysed in the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratorium, Munich, Germany. Results: The resonance states previously reported at $E_\mathrm{x} = 8862$, $8894$ and $9000$ keV in other experiments were not observed in the present experiment at any angle. This result, combined with other non-observations 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 $E_\mathrm{x} = 8862$, $8894$ and $9000$ keV are unlikely to exist and should be omitted from future evaluations of the $^{22}$Ne($p,γ$)$^{23}$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 non-selective information of the excited states of nuclei.