First inverse kinematics measurement of key resonances in the ${}^{22}\text{Ne}(p,\gamma)^{23}\text{Na}$ reaction at stellar temperatures

In this Letter we report on the first inverse kinematics measurement of key resonances in the ${}^{22}\text{Ne}(p,\gamma)^{23}\text{Na}$ reaction which forms part of the NeNa cycle, and is relevant for ${}^{23}$Na synthesis in asymptotic giant branch (AGB) stars. An anti-correlation in O and Na abundances is seen across all well-studied globular clusters (GC), however, reaction-rate uncertainties limit the precision as to which stellar evolution models can reproduce the observed isotopic abundance patterns. Given the importance of GC observations in testing stellar evolution models and their dependence on NeNa reaction rates, it is critical that the nuclear physics uncertainties on the origin of ${}^{23}$Na be addressed. We present results of direct strengths measurements of four key resonances in ${}^{22}\text{Ne}(p,\gamma)^{23}\text{Na}$ at E$_{{\text c.m.}}$ = 149 keV, 181 keV, 248 keV and 458 keV. The strength of the important E$_{{\text c.m.}}$ = 458 keV reference resonance has been determined independently of other resonance strengths for the first time with an associated strength of $\omega\gamma$ = 0.439(22) eV and with higher precision than previously reported. Our result deviates from the two most recently published results obtained from normal kinematics measurements performed by the LENA and LUNA collaborations but is in agreement with earlier measurements. The impact of our rate on the Na-pocket formation in AGB stars and its relation to the O-Na anti-correlation was assessed via network calculations. Further, the effect on isotopic abundances in CO and ONe novae ejecta with respect to pre-solar grains was investigated.

In this Letter we report on the first inverse kinematics measurement of key resonances in the 22 Ne(p, γ) 23 Na reaction which forms part of the NeNa cycle, and is relevant for 23 Na synthesis in asymptotic giant branch (AGB) stars. An anti-correlation in O and Na abundances is seen across all well-studied globular clusters (GC), however, reaction-rate uncertainties limit the precision as to which stellar evolution models can reproduce the observed isotopic abundance patterns. Given the importance of GC observations in testing stellar evolution models and their dependence on NeNa reaction rates, it is critical that the nuclear physics uncertainties on the origin of 23 Na be addressed. We present results of direct strengths measurements of four key resonances in 22 Ne(p, γ) 23 Na at Ec.m. = 149 keV, 181 keV, 248 keV and 458 keV. The strength of the important Ec.m. = 458 keV reference resonance has been determined independently of other resonance strengths for the first time with an associated strength of ωγ = 0.439 (22) eV and with higher precision than previously reported. Our result deviates from the two most recently published results obtained from normal kinematics measurements performed by the LENA and LUNA collaborations but is in agreement with earlier measurements. The impact of our rate on the Na-pocket formation in AGB stars and its relation to the O-Na anti-correlation was assessed via network calculations. Further, the effect on isotopic abundances in CO and ONe novae ejecta with respect to pre-solar grains was investigated.
Globular clusters (GCs) are dense aggregates of predominantly old stars found in the galactic halo. These objects have long fascinated astronomers for the unique insight they provide into the processes driving galaxy formation and chemical evolution. In particular, GCs are ideal test sites for answering open questions about the interplay between primordial and evolutionary chemical enrichment [1]. These objects have therefore warranted significant observational efforts and, through recent studies a complex picture of GCs abundance patterns has emerged, with strong evidence supporting multiple epochs of star formation [2]. Despite clear variability in observed abundances, some ubiquitous trends become apparent, such as the anti-correlation in oxygen and sodium abundances [3]. Currently stellar models are unable to reproduce many of the abundance patterns in GC stars along the red-giant branch (RGB), but absent in their field star counterparts. AGB stars undergoing Hot Bottom Burning (HBB) are currently the most favored astrophysical sites used to explain the O-Na anticorrelation [4,5]. HBB occurs during the quiescent phase between two thermal pulses (TP) when part of the Hshell is included in the envelope convection and the Hshell has enhanced access to fuel which is convectively mixed into its outer layers. In TP-AGB stars, sodium is primarily synthesized by proton-capture on 22 Ne in the outer-most layer of the core-envelope transition zone, resulting in the formation of a so-called 23 Na pocket on top of the 14 N pocket [6,7]. The 23 Na pocket forms when 22 Ne and 12 C abundances are comparable, and the 22 Ne(p, γ) 23 Na and 12 C(p, γ) 13 N reactions compete. In low-mass AGB stars, at solar metallicity, models predict the 23 Na pocket to be the main sodium source, and the overproduction of Na to result from the ingestion of arXiv:1910.00791v2 [nucl-ex] 4 Oct 2019 the 23 Na pocket during the thermal dredge up [6]. The 22 Ne(p, γ) 23 Na reaction further affects the 20 Ne/ 22 Ne, 21 Ne/ 22 Ne and 20 Ne/ 21 Ne abundance ratios of pre-solar grains found in meteorites. These grains are important signatures of nucleosynthesis in different stellar environments and mixing in stellar ejecta before the formation of our solar system. The 22 Ne(p, γ) 23 Na reaction is also influential in nova nucleosynthesis, where a sensitivity study by Iliadis [8] showed that this reaction rate -varied within uncertainties -can affect the final abundances of 22 Ne and 23 Na by factors of ∼100 and ∼7, respectively.
In recent years the 22 Ne(p, γ) 23 Na reaction has been targeted intensively by three facilities, all employing normal kinematics techniques [9][10][11][12]. The low-energy regime was investigated by the LUNA and LENA collaborations, since the rate is dominated by narrow low-energy resonances. With the exception of the low-energy resonance strength measurements by LUNA [11,12] with E c.m. ≤ 248 keV, all previously reported strengths were either measured relative to reference resonances at E c.m. = 458 keV or 1222 keV or depended on these resonances to determine target stoichiometries. The 458 keV resonance strength directly influences the strengths of the low-energy resonances reported by LENA [10], and was used as reference for target stoichiometries in 22 Ne+α studies [13] and normal kinematics measurements of the 22 Ne(p, γ) 23 Na reaction [9]. Moreover, the 458 keV resonance is particularly relevant for reaction-rate compilations conducted by Iliadis et al. [14], for which all other measured resonance strengths were normalized to the 458 keV strength value of ωγ = 0.524(51) eV [15]. The latter was determined relative to the E p = 405.5(3) keV (ωγ = (8.63(52)×10 −3 ) eV [16]) resonance strength in the 27 Al(p, γ) 28 Si reaction, and depends on the background contribution of the E p = 326 keV and 447 keV resonances in the same reaction. We note that there is a more recent result for the E p = 405.5(3) keV resonance of ωγ = 1.04(5)×10 −2 eV [17]. Using this value for a linear re-normalization would reduce the 458 keV strength reported by Longland et al. by ∼17% to ωγ = 0.435(42) eV. Further, the strengths of the resonances affecting the background in that measurement have also been normalized to the 405.5(3) keV resonance. Though the 458 keV resonance strength has been investigated numerous times [9,15,18], our measurement reveals that the situation for this resonance is still not resolved. In fact, the strength of this resonance has never been measured independently of other resonances. However, this work puts forward a direct, reference-independent measurement which is largely independent of knowledge of the relevant branching ratios (BRs).
In this Letter we report on the first inverse kinematics measurement of the 22 Ne(p, γ) 23 Na reaction, which comprises the strength determination of the to-date largest set of resonances for this reaction measured within one experiment, covering an energy range from E c.m. = 149 keV to 1.222 MeV.
The measurement was performed using the DRAGON (Detector of Recoil and Gammas Of Nuclear reactions) recoil separator [19] located at the ISAC beam facility at TRIUMF, Vancouver, Canada. DRAGON is designed to conduct studies of radiative capture reactions in inverse kinematics and consists of three main sections: (1) a windowless, differentially pumped, recirculated gas target surrounded by a high-efficiency γ-detector array consisting of 30 BGO detectors; (2) a high-suppression electromagnetic mass separator with two stages of charge and mass selection; (3) a variable heavy ion detection system in combination with two micro-channel plate (MCP) based timing detectors for time-of-flight (TOF) measurements. The recoil-detection system consisted of a doublesided silicon strip detector (DSSSD) [19,20].
A high intensity (∼2 × 10 12 ions/sec) isotopically pure 22 Ne 4+ beam was delivered to the hydrogen-filled gas target. 23 Na recoils were transmitted through the separator and detected in the DSSSD. To contain the entire yield profile of the resonances within the target, an average H 2 gas pressure of 5 Torr was used, corresponding to a target thickness of ∼3.9×10 18 hydrogen atoms/cm 2 . The maximum charge state at each energy was selected by transmitting the beam through the magnetic dipoles. Charge-state distributions for 23 Na ions in hydrogen gas at the recoil energies were measured to eliminate systematic uncertainties associated with semi-empirical calculations. Two silicon surface barrier detectors positioned at 30 • and 57 • relative to the beam axis inside the target detected elastically scattered protons for a relative measure of the beam intensity. The elastic scattering rate was normalized to automated hourly Faraday Cup readings. Prior to each yield measurement, the energy loss across the target was determined by measuring the incoming and outgoing beam energy via the magnetic field of the first magnetic dipole, which centered the beam on-axis on a pair of current sensitive slits. The incoming beamenergy spread was ∼0.1% FWHM [21]. Stopping powers ( ) were calculated based on the measured energy loss, the gas density derived from continuously recorded pressure and temperature, and the effective target length [19]. This reduces uncertainties induced by the commonly used software packages SRIM [22] and LISE [23]. Resonance energies were determined via the position sensitive BGO array by relating the centroid of the distribution (γ yield vs target position) to the incoming and outgoing beam energy [21]. For improved background suppression, the resonance strengths were extracted in a coincidence analysis, where the GEANT3 [24] simulation used to determine the BGO detection efficiency relies on literature BRs. For the 458 keV yield measurement the DSSSD energy spectrum was fitted with a double Gaussian function to set appropriate energy cuts for the "golden" recoil gate at ±3.5σ relative to the peak centroids, and to account for the satellite peak at the low energy side of the main recoil peak (Fig. 1). The satellite peak results from the additional energy loss of ions passing the 3% aluminum DSSSD grid [25]. Including the satellite peak and accounting for inter-strip events results in a DSSSD effi- ciency of (96.15 ± 0.1 stat. ± 0.43 sys. )% [25]. The established DSSSD and BGO energy gates were then placed on the separator TOF spectrum to extract the number of recoils. The background within the recoil region was estimated by sampling the time-random background and calculating an average expectation value over the width of the signal region. A poissonian background model was chosen as the probability to count a random coincidence in the separator TOF spectrum follows Poisson statistics. High statistics and a clear separation of unreacted beam and recoils (Fig. 1) also allowed for a singles analysis of the 458 keV resonance to eliminate uncertainties introduced by the dependence of the coincidence analysis on BRs and BGO detection efficiency. Using the fit parameters of the coincidence spectrum as guide for the singles analysis, a triple Gaussian function was applied to the DSSSD energy spectrum, and the integral of the main recoil peak and satellite peak comprises the number of recoil events. Figure 2 presents the 458 keV resonancestrength values based on coincidence and singles analysis, which are mutually consistent, relative to previous measurements.
Our result for the 458 keV resonance strength of ωγ coinc = 0.441(50) eV (ωγ singles = 0.439(22) eV) is lower and not in agreement within errors with the two latest results [9,18]. However, it is in agreement with three previous values [15,26,27]. The result from Meyer et al. [27] was normalized to the E c.m. = 612 keV resonance strength, and the Endt et al. value is based on Ref. [27], however, normalized the E c.m. = 1.222 MeV resonance strength from Ref. [28]. The sensitivity of former studies to reference resonances underlines the necessity of reference-independent measurements as well as more precise measurements of reference-resonance strengths.
To determine the 149 keV, 181 keV and 248 keV resonance strengths, conservative recoil gates for DSSSD and BGO energy were placed on the separator TOF vs MCP TOF spectrum or separator TOF spectrum (Fig. 3) 248 keV yield measurement does not have an associated separator vs MCP TOF spectrum since the MCP detection efficiency was too low to give enough statistics; this issue was later resolved for the lower energy measurements.
For the analysis of the 149 keV and 181 keV yield measurements the branching ratios for the E x = 8943(3) keV and 8972(3) keV levels given in Ref. [10] were used for the GEANT3 simulation. The BRs from Ref. [10] were chosen over those reported in Ref. [29] as the analysis in Ref. [10] did not require additional background subtraction or corrections for coincidence-summing effects, and accounted for escape peaks and Compton continuum.
For the 149 keV resonance we report a strength of ωγ(149) = (1.67 ± 0.028 (sys) +0.039 −0.028 (stat))×10 −7 eV, which is lower but in agreement with all previously published values. Our 181 keV resonance strength of ωγ(181) = (2.17 +0. 32 −0.31 (sys) +0.2 −0.17 (stat))×10 −6 eV is in good agreement with the LUNA HPGe result [12] and lower but also in agreement with the LENA result. However, our result is 20% lower than the LUNA BGO measurement [11] (compare Tab. I). Regarding the 248 keV resonance we report a strength of ωγ = 8.5(1.4)×10 −6 eV. The dominant contributions to the systematic uncertainty result from uncertainties on coincidence efficiency (10%), stopping power (4.3 -5.9%), charge-state fraction (1.8%(181 keV) -2.4%(149 keV)), MCP efficiency (5%) and beam normalization (1.1 -4.9%). To clarify that there is no trend in systematically lower strengths values relative to the LUNA results, we note that the DRAGON results for higher energy resonances are either in agreement with previous results or slightly higher, and will be published elsewhere [30]. In view of the significant deviation of the DRAGON ωγ(458 keV) result from the value used to normalize the strengths of the low-energy resonances in the TUNL measurement [10], one has to carefully review the latter. In fact, re-normalizing the LENA 149 keV strength to our ωγ(458 keV) result, brings it into better agreement with the DRAGON measurement, and a re-normalized LENA value for the 181 keV resonance is compatible with the DRAGON and LUNA HPGe results. Figure 4 displays an overlay of the rates determined    [10] Ref. [10] renormalized to this work 181 1.75(29)×10 −6 149 1.53(33)×10 −7 from this work and those of LUNA and LENA, normalized to the STARLIB2013 rate [31]. The dramatic enhancement of the LUNA rate is mainly due to the inclusion of the E c.m. = 100 keV resonance, for which only an upper limit has been reported [11,32]. Our rate maps closely with the LENA rate, with a slight reduction due to our reduced 149 keV and 181 keV strengths. The effect of the DRAGON rate compared to the Iliadis 2010 rate [14] on the sodium and neon abundances in neon-oxygen (ONe) novae with underlying white-dwarf (WD) masses of 1.15 M and 1.25 M , as well as carbonoxygen (CO) novae (1.15 M and 1.00 M ) was investigated using hydro-dynamical nova models [33,34]. Changes of more than 10% in the isotopic abundances within the Ne-Al region ( 20,21,22 Ne, 22,23 Na, 25,26 Mg, 26,27 Al) in 1.15 M CO novae, and a factor of 2 enhancement in 23 Na abundance are observed for both CO nova models. For ONe novae, a reduction of the 22 Ne content by a factor of 2 is observed for both WD mass models. Further, the 24 Mg abundance is enhanced by ∼15% in the 1.25 M model, whereas only slight differences are seen for the remaining isotopes considered in both models. Regarding CO novae, the new rate underlines the differences in the 25 Mg/ 26 Mg and 26 Mg/ 25 Mg ratios between the 1.0 and 1.15 M models. Our rate leads to an increase of 24% in the isotopic ratio of 25 Mg/ 24 Mg, and to a decrease of 13% in the 26 Mg/ 25 Mg ratio for the 1.15 M model relative to the STARLIB2013 rate. This can be explained by the sensitivity of Mg synthesis to the peak temperature [35]. Due to the larger rate the mass flow is pushed up to Mg synthesis temperatures. As a result of this correlation these ratios become relevant in the identification of pre-solar grains which have a putative CO novae origin, as they function as probe for the peak temperature reached in the outburst, and the underlying WD mass. In a sensitivity study [8], the final abundances of 24,25 Mg for 1.15 M CO novae varied by up to a factor of 5, when varying the 22 Ne(p, γ) 23 Na rate within its uncertainties, whereas the new rate strongly limits the reaction rate uncertainty in the temperature range of interest (T peak = 170 MK). Varying the new rate within its limits only changes the Mg isotope mass fractions by up to 7%. For ONe novae, the cycling back to 20 Ne is irrelevant for both the 1.15 and 1.25 M model, as 20 Ne is sufficiently available. This is reflected in the same 20,21 Ne final yield, independent of the model. Though differences in the 22 Ne abundance are found, abundances of 23 Na, 24 Mg or higher mass isotopes remain unaffected. Instead, the observed difference in 22 Ne abundances may be relevant for studies of pre-solar grains, which are identified by noble gas ratios. The Nu-Grid multi-zone post-processing code MPPNP [36] was used to implement our rate in nucleosynthesis network calculations, and to model the [Na/Fe] abundance ratio on the AGB star surface at the end of the evolution of stable isotopes for various masses and metallicities. A 5 M model with metallicity z = 0.006 was utilized to study the impact of our rate on HBB in TP-AGB stars, using the STARLIB2013 rate as reference. We observe a close mapping of [Na/Fe] as a function of [s/Fe] for the two rates, confirming the robustness of the STARLIB2013 rate. The effect of the 22 Ne(p, γ) 23 Na and 22 Ne(n, γ) 23 Ne rates on the sodium abundance was studied. Without the (p,γ) channel, the abundance drops to almost zero, confirming the 22 Ne(p, γ) 23 Na reaction as main production channel of sodium in massive AGB stars. Further, the effect on the 23 Na-pocket in low-mass AGB stars for a 2M model (at Z = 0.001 and Z = 0.006) formed with the DRAGON rate relative to the STARLIB2013 rate was investigated by evaluating the abundance profile of 23 Na when the pocket is fully formed (Fig. 5). Switching off the 22 Ne(p, γ) 23 Na reaction results in a significant abundance reduction. However, in contrast to the 5 M model, the abundance stays relatively high due to the second production channel 22 Ne(n,γ) 23 Ne(β − ) 23 Na. At T = 100 MK, we find a factor of 4 enhanced rate relative to the STARLIB2013 rate. However, the differences between the results obtained with the 22 Ne(p, γ) 23 Na STARLIB2013 and DRAGON rate are minor, showing that the abundance does not directly correlate with rate variations. This is not in agreement with the factor of 3 enhancement in 23 Na production stated by Slemer et. al. [37] based on the LUNA rate, which includes the tentative 68 keV and 100 keV resonances. Even though Slemer et. al. use a code that couples mixing and burning during HBB, and adopt a similar list of isotopes as NuGrid, neutron captures are not included. Thus, the important 23 Na destruction channel 23 Na(n, γ) 24 Na stated in Ref. [38] is not considered.
In summary, key resonances in the 22 Ne(p, γ) 23 Na reaction have been investigated in inverse kinematics for the first time using the DRAGON recoil separator. The strength of the important reference resonance at E c.m. = 458 keV has been determined with higher precision via a direct measurement, and does not agree within errors with the two most recent normal kinematics results. Our result affects resonance strengths that have been determined relative to the strength of this resonance, as well as neon-target stoichiometries determined based on its strength. A new reaction rate was calculated based on the DRAGON measurement, which confirms the accuracy of the current 23 Na production results in AGB stars in relation to the behavior of the 22 Ne(p, γ) 23 Na reaction and underlines the importance of this reaction for the sodium production in AGB stars. Further work is needed to reassess the sensitivity of Mg isotopic ratios in CO novae to rate variations of isotopes in the Ne-Al region to use said ratios as a probe of the underlying WD peak temperatures.