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

TL;DR

This study used proton inelastic scattering to investigate suspected resonance states in $^{23}$Na, finding no evidence for these states and thus clarifying the nuclear reaction rates relevant to stellar nucleosynthesis.

Contribution

The paper provides experimental evidence against the existence of previously reported resonance states in $^{23}$Na, refining the nuclear data used in astrophysical models.

Findings

Resonance states at 8862, 8894, and 9000 keV were not observed.

Results strongly suggest these states do not exist.

Clarifies reaction rates for astrophysical models.

Abstract

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($p,\gamma$)$^{23}$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($p,\gamma$)$^{23}$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($p,\gamma$)$^{23}$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.

Full text

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 22Ne($p,\gamma$)23Na 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 22Ne($p,\gamma$)23Na measurements.

Purpose

To study excited states in 23Na above the proton threshold to determine if the unconfirmed resonance states in 23Na exist.

Methods

The non-selective proton inelastic scattering reaction at low energies was used to search for excited states in 23Na 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 22Ne($p,\gamma$)23Na 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.

††preprint: APS/123-QED

I Astrophysical Background

Globular clusters (GCs) are large populations of stars bound together by gravity. Since GCs are considered to be formed and evolved without external factors, they are one of the most important laboratories for understanding stellar evolution. In contrast to what was believed years ago, they are composed of multiple populations of stars [1, 2] and are observed to exhibit anomalous abundance trends in elements from C to Al that are not seen in field stars. These abundance anomalies challenge our understanding of how GCs have formed and evolved, with some unknown polluting site or sites [3, 4, 5, 6, 7, 8, 9, 10, 11, 12] within the GCs causing significant star-to-star variations. Suggested polluting sites include low-mass stars, AGB and super-AGB stars, massive and supermassive stars, and classical novae based on carbon-oxygen or oxygen-neon white dwarfs (see Refs. [1, 13] for evaluations of possible sites).

One of the most uncertain abundance patterns is the sodium-oxygen anti-correlation [14, 2]. The abundance of 23Na has a significant impact on this anti-correlation; the 22Ne($p,\gamma$)23Na reaction, found in the NeNa cycle of hydrogen burning, has a large effect on the abundance of 23Na along with other reactions such as 23Na($p,\gamma$)24Mg, 23Na($p,\alpha$)20Ne [15, 16, 17].

Different facilities have studied the 22Ne($p,\gamma$)23Na reaction and 23Na resonance states. Direct measurements of resonance strengths within the astrophysical region of interest are challenging. Indirect measurements, such as $\gamma$-ray spectroscopy and single-proton transfer reactions have provided valuable constraints on the reaction rate. Significant uncertainties of up to an order of magnitude in the reaction rate at temperatures relevant to AGB stars and Hot-Bottom Burning ($T<0.1$ GK) remain due to unclear nuclear data; the reaction rate at temperatures relevant to classical novae is rather well constrained [14, 18, 19].

Direct measurements of resonance strengths have extended down to $E_{\mathrm{c.m.}}=65$ keV. The direct measurements performed at the Laboratory for Undeground Nuclear Astrophysics [2, 18], the Laboratory for Experimental Nuclear Astrophysics [20, 21, 22] and the DRAGON recoil separator at TRIUMF [23, 14] have provided resonance strengths or upper limits of resonance strengths for most known resonance states [24, 25, 26]. However, three resonances corresponding to states reported by Powers et al. [27] at $E_{\mathrm{x}}=8862$, $8892$ and $9000$ keV ($E_{\mathrm{r,c.m.}}=68$, $100$ and $206$ keV, $E_{\mathrm{r,lab}}=71$, $105$ and $215$ keV) have not been observed. In fact, the LUNA direct measurements have ruled out the $E_{\mathrm{x}}=8892$- and $9000$-keV resonance strengths as being astrophysically important. However, even with the stringent limit of $\omega\gamma_{\mathrm{68}}<6\times 10^{-11}$ eV (at 90% confidence) on the strength of the $E_{\mathrm{r,c.m.}}=68$-keV resonance provided by Ferraro et al. [18], the 22Ne($p,\gamma$)23Na reaction rate is uncertain by a factor of ten depending on the existence of this state.

This paper reports an experimental study of the 23Na($p,p^{\prime}$)23Na proton inelastic-scattering reaction with a beam energy of $E_{p}=14$ MeV using the Q3D magnetic spectrometer at Munich [28] to momentum analyse the scattered particles. At this energy, the proton inelastic scattering reaction is rather insensitive to the structure of the excited states enabling a stringent test of the existence of possible resonance states at $E_{\mathrm{x}}=8862$, $8892$ and $9000$ keV. Section II discusses the applicability of the ($p,p^{\prime}$) reaction as an unselective probe to search for 23Na states of interest. Section III details the experimental methodology and data analysis procedures. Our results are then presented and discussed in Section IV, with concluding remarks given in Section V.

II The ($p,p^{\prime}$) reaction

The ($p,p^{\prime}$) reaction has a long history of being used to perform simple spectroscopy to identify states at the energy used in this experiment ($E_{p}=14$ MeV) and in similar past experiments [29, 25, 30, 31, 32]. One of the primary features of this reaction is that it appears to be non-selective, unlike many of the other reactions used for these experiments such as, e.g. 22Ne(${}^{3}\mathrm{He},d$)23Na which is sensitive to the 22Ne$+p$ structure of the 23Na states. The evidence for the selectivity of the reaction is empirical; the outline of why this reaction is believed to have weak or no selectivity to the structure of the excited states is summarised below.

Measurements of the 27Al($p,p^{\prime}$)27Al reaction have with the Orsay SplitPole and the Munich Q3D [30, 31] observed every known state in 27Al between the ground state and the 23Na$+\alpha$ threshold at $S_{\alpha}=10091.8(1)$ keV. The Q3D measurement, which will be the subject of a future publication reports angular distributions which are flat and featureless, implying that the reaction proceeds through a compound process. This is possibly due to the outgoing protons having energies ($4.3$ and $5.1$ MeV) just above the Coulomb barrier height ($V_{\mathrm{Coulomb}}=3.3$ MeV) meaning that compound processes dominate over direct ones. One result of this is that no information may be obtained about the spins and parities of the states populated since the characteristic diffraction patterns obtained in higher-energy inelastic scattering, dominated by direct processes, are absent.

All known isolated states between the ground state and the 23Na$+\alpha$ threshold at $S_{\alpha}=10091.8(1)$ keV were observed in Ref. [30]. This is in contrast to the suggestion of Moss and Sherman [29] that there is a strong antiselectivity to $J=\frac{1}{2}$ states in the ($p,p^{\prime}$) reaction based on the non-observation of a number of levels in that study. The cause of this disagreement is unclear though we note that the studies of Benamara et al. [30] and Adsley et al. [32] observed a number of additional states in 27Al (Benamara) and 26Mg (Adsley) which were not observed by Moss and Sherman [29] and Moss [25], suggesting that the experimental conditions may have played a role in their conclusion regarding the antiselection to $J=1/2$ states.

Finally, we note that this proton scattering reaction is not a resonance reaction of the form 22Ne$+p$ and this means that the cross sections for populating 23Na states are not thought to be proportional to the proton widths for those 23Na states. This means that the 22Ne$+p$ widths required for the 22Ne($p,\gamma$)23Na resonance strengths and subsequently reaction rates cannot be deduced from these data.

III Experimental details and data analysis

A 14-MeV proton beam from the tandem accelerator at the Maier-Leibnitz Laboratorium was transported to the target of the Q3D spectrograph [28]. The target used to probe 23Na states consisted of around 50 $\mu$g/cm2 of NaF on a 20 $\mu$g/cm2 carbon backing. In order to quantify the background from instrumental effects and target contamination, scattering from a carbon foil similar to the backing of the NaF target was also measured. A LiF target was used to identify 19F states but only for the 70-degree data.

Reaction products were momentum analyzed by the Munich Q3D and detected at the focal plane in a detector consisting of two gas-proportional counters backed by a plastic scintillator (for details about the focal-plane detector and similar devices see Refs. [33]). Data were collected at five scattering angles: 25, 35, 40, 50, and 70 degrees. Data from different angles are used to identify peaks in the focal plane coming from target contaminants. Target contaminants appear to move in excitation energy with changing angle due to different kinematic shifts. This shift technique has been used to identify contaminating states in other reactions such as the 26Mg($p,p^{\prime}$)26Mg reaction where a small amount of 24Mg contamination was present in the target and the resulting peaks could be identified and rejected through the kinematic shift [32].

The focal-plane position was related to the magnetic rigidity using known states in 16O, 19F and 23Na for calibration. For the 70-degree data, the focal-plane to rigidity calibration for these states is shown in Fig. 1. The corresponding 23Na excitation-energy spectrum is shown in Fig. 2 along with the $3\sigma$ uncertainty bands for the excitation energy. Similar calibrations to 23Na, 19F and 16O states were performed for other angles. The resulting $E_{\mathrm{x}}$ spectra and uncertainty bands are shown in Figs. 3-6. Each of the calibrations included at least one state from a different nucleus (19F from the NaF targets and oxygen contamination in the carbon targets to verify the assigned 23Na levels in the calibrations). Information on the states used to calibrate at each angles is given in the figure captions.

The increase in the excitation-energy uncertainty at higher excitation energies is due to the increased uncertainty in the excitation energies of the states used in the calibration at the low-rigidity (high-excitation energy) end of the focal plane. At these higher excitation energies, the $E_{\mathrm{x}}=9072(3)$-keV state in 23Na has been used for the calibration when possible. However, since the excitation energy of this state has a $3$-keV uncertainty, the corresponding uncertainty band in the present experiment is of the same size.

IV Discussion

There are three tentative resonance states listed in this excitation-energy region in 23Na: at $E_{\mathrm{x}}=8862$, $8894$ and $9000$ keV, note that no uncertainties were given in the original study which claimed these tentative resonances. Around the tentative $E_{\mathrm{x}}=8862$- and $8894$-keV states the spectrum is notably featureless. Both of the tentative states are well resolved from other known 23Na levels. It is unlikely that these resonance states exist.

The $E_{\mathrm{x}}=9000$-keV state is located in a region with multiple populated levels, including contaminant states from other nuclei including 19F. Since there is no state populated at multiple angles with consistent excitation energy, we also conclude that this state has not been populated in this experiment and that it is unlikely to exist.

In this experiment, we have not observed a state at $E_{\mathrm{x}}=8963.9(11)$ keV which has been assigned in $\gamma$-ray decays following the 12C(12C$,p$)23Na fusion-evaporation reaction in coincidence with the $E_{\gamma}=440$-keV transition from the decay of the first excited state in 23Na [26, 35]. It is possible that the $\gamma$-ray is feeding the $J^{\pi}=7/2^{+}$ state at $E_{\mathrm{x}}=2075.9(4)$ keV and subsequent the $E_{\gamma}=1636$-keV transition was not observed and so the excitation energy of this state has been misplaced in those $\gamma$-ray studies, though this is not confirmed [36]. Alternatively, if the state is weakly populated in the present experiment then its close proximity to the $E_{\mathrm{x}}=8946.8(6)$-keV may make it hard to observe.

V Conclusions

The major remaining uncertainty in the 22Ne($p,\gamma$)23Na reaction rate contributing to the Na-O anticorrelation observed in globular clusters is the existence of a state at $E_{\mathrm{x}}=8862$ keV, corresponding to a resonance energy of $E_{\mathrm{r,c.m.}}=68$ keV. A strong contribution of the potential $E_{\mathrm{r,c.m.}}=100$-keV and $E_{\mathrm{c.m.}}=206$-keV resonances (from purported states at $E_{\mathrm{x}}=8894$ and $9000$ keV) to the reaction rate had previously been ruled out by previous direct measurements which provide a tight upper limit on the resonance strength of these resonances (see e.g. Ref. [18]). The influence of the $E_{\mathrm{r,c.m.}}=68$-keV resonance on the reaction rate remained an open question largely due to the lower resonance energy. In the present measurement, which used the non-selective 23Na($p,p^{\prime}$)23Na reaction to populate excited states in 23Na, none of the potential resonance states are observed, in agreement with other direct and indirect studies of the excited levels of 23Na. Only one study reports these tentative resonance states [27] and multiple studies using different experimental probes [24, 2, 18] including the present one see no evidence for them. These results strongly indicate that the potential resonance states do not exist (though it is not possible to prove that) and should be omitted from evaluations of the reaction rates until and unless conclusive evidence may be obtained for the existence of these states. Efforts to directly measure these resonances are unlikely to observe any signal above the direct-capture contribution. Finally, we recommend using the reaction-rate evaluation of Ref. [14] and its associated uncertainties for future astrophysical models, reducing the reaction-rate uncertainty in the temperature range of hot-bottom burning from an order of magnitude to 40%.

Acknowledgements.

The authors thank the beam operators at the Maier-Leibnitz Laboratorium for their work and support and the target preparation laboratory of INFN-LNS for sample and target preparation and characterisation. DPCR thanks the Department of Energy Nuclear Physics grant number DE-FG02-93ER40773 and DE-SC0022469, the Texas Research Expanding Nuclear Diversity (TREND) program, the Cyclotron Institute at Texas A&M University. MW acknowledges support provided by the Natural Sciences & Engineering Research Council of Canada grant SAPPJ-2019-00039. PA thanks the Claude Leon Foundation for support during his time at the University of the Witwatersrand and iThemba LABS in the form of a postdoctoral fellowship. PA also thanks David Jenkins of the University of York for useful comments relating to the 12C(${}^{12}\mathrm{C},p$)23Na Gammasphere data and Richard Longland of North Carolina State University for useful comments and references regarding 22Ne($p,\gamma$)23Na direct measurements.