First inverse kinematics study of the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction and its role in AGB star and classical nova nucleosynthesis

Background: Globular clusters are known to exhibit anomalous abundance trends such as the sodium-oxygen anticorrelation. This trend is thought to arise via pollution of the cluster interstellar medium from a previous generation of stars. Intermediate-mass asymptotic giant branch stars undergoing hot bottom burning (HBB) are a prime candidate for producing sodium-rich oxygen-poor material, and then expelling this material via strong stellar winds. The amount of ${}^{23}\mathrm{Na}$ produced in this environment has been shown to be sensitive to uncertainties in the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rate. The ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction is also activated in classical nova nucleosynthesis, strongly influencing predicted isotopic abundance ratios in the Na-Al region. Therefore, improved nuclear physics uncertainties for this reaction rate are of critical importance for the identification and classification of pre-solar grains produced by classical novae.

Purpose: At temperatures relevant for both HBB in AGB stars and classical nova nucleosynthesis, the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rate is dominated by narrow resonances, with additional contribution from direct capture. This study presents new strength values for seven resonances, as well as a study of direct capture.

Method: The experiment was performed in inverse kinematics by impinging an intense isotopically pure beam of ${}^{22}\mathrm{Ne}$ onto a windowless ${\mathrm{H}}_2$ gas target. The ${}^{23}\mathrm{Na}$ recoils and prompt $\gamma$ rays were detected in coincidence using a recoil mass separator coupled to a $4\pi$ bismuth-germanate scintillator array surrounding the target.

Results: For the low-energy resonances, located at center of mass energies of 149, 181, and 248 keV, we recover stength values of $\omega {\gamma }_{149}=0.{17}_{-0.04}^{+0.05}, \omega {\gamma }_{181}=2.2\pm 0.4$, and $\omega {\gamma }_{248}=8.2\pm 0.7 \mu \text{eV}$, respectively. These results are in broad agreement with recent studies performed by the LUNA and TUNL groups. However, for the important reference resonance at 458 keV we obtain a strength value of $\omega {\gamma }_{458}=0.44\pm 0.02$ eV, which is significantly lower than recently reported values. This is the first time that this resonance has been studied completely independently from other resonance strengths. For the 632-keV resonance we recover a strength value of $\omega {\gamma }_{632}=0.48\pm 0.02$ eV, which is an order of magnitude higher than a recent study. For reference resonances at 610- and 1222-keV, our strength values are in agreement with the literature. In the case of direct capture, we recover an $S$ factor of 60 keV b, consistent with prior forward kinematics experiments.

Conclusions: In summary, we have performed the first direct measurement of ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ in inverse kinematics. Our results are in broad agreement with the literature, with the notable exception of the 458-keV resonance, for which we obtain a lower strength value. We assessed the impact of the present reaction rate in reference to a variety of astrophysical environments, including AGB stars and classical novae. Production of ${}^{23}\mathrm{Na}$ in AGB stars is minimally influenced by the factor of 4 increase in the present rate compared to the STARLIB-2013 compilation. The present rate does however impact upon the production of nuclei in the Ne-Al region for classical novae, with dramatically improved uncertainties in the predicted isotopic abundances present in the novae ejecta.

Figure 1

Schematic of the DRAGON recoil separator. The electromagnetic elements, slit positions, and Faraday cups are labeled.

Figure 2

Normalized charge-state fractions for each charge state as a function of outgoing ${}^{23}\mathrm{Na}$ energy. The distributions are fit with the semi-empirical formula of Liu et al. [38], with the shaded regions indicating the $1\sigma$ confidence limits of the fits. The $3^{+}$ fit did not converge due to a lack of data points on the rising portion of the distribution. Instead, the $q=3^{+}$ recoil charge-state fraction, utilized for the $E_{\mathrm{c}.\mathrm{m}.}=149$-keV yield measurement, was determined after the experiment at the outgoing recoil energy. The dashed blue curve is simply to guide the eye.

Figure 3

Separator time-of-flight (TOF) spectra for resonant yield measurements at $E_{\mathrm{c}.\mathrm{m}.}=$ 1222 keV (a), 632 keV (b), 610 keV (c), 458 keV (d), and 248 keV (e). The spectrum shown in the bottom-right panel (f) pertains to the lowest-energy nonresonant yield measurement at $E_{\mathrm{c}.\mathrm{m}.}=282$ keV. The separator TOF is constructed from the time difference between a “head” event recorded by the BGO array and a “tail” event recorded by any of the focal plane detectors. The background rate within the signal region, bound by the vertical red dashed lines, was estimated by sampling the uniform background outside of the signal region.

Figure 4

DSSD front strip energy spectra for the yield measurements at $E_{\text{c.m.}}=$ 1222 keV (a), 632 keV (b), and 458 keV (c). Both singles (back line histograms) and coincidence (gray-filled histograms) events are shown. The vertical red dashed lines indicate the DSSD energy cuts imposed on the data. The spectra for the 632- and 458-keV yield measurements exhibit some leaky-beam contamination at the focal plane; as evidenced by the small peak at higher energy compared to the more prominent recoil peak. These events are entirely suppressed in coincidences, as one would expect. To calculate the singles yield, these events were subtracted from the total number of recoils by fitting to a Gaussian (black dashed curve) and integrating over the cut region. The energy cut is slightly expanded to lower energies to include recoils that exhibit additional energy loss through the aluminium contact grid covering the DSSD surface [34]. The red solid lines on the $E_{\mathrm{c}.\mathrm{m}.}=632$- and 458-keV plots represent a triple-Gaussian fit across the signal region, accounting for all the aforementioned features in the singles data. Such a fit was unnecessary to perform on the 1222-keV data as leaky-beam contamination was negligible, meaning that no background subtraction was required.

Figure 5

Comparison between present and literature values for the 458-keV resonance. The blue solid triangles indicate re-normalized values for the Kelly [24] and Longland [45] measurements if one instead adopts the $E_r=394$-keV ${}^{27}\mathrm{Al}+p$ reference resonance reported in Ref. [50], as opposed to the strength reported in Ref. [51] (see text for details).

Figure 6

(Top panel) MCP TOF vs. separator TOF for the on resonance yield measurement at $E_{\mathrm{c}.\mathrm{m}.}=181$ keV, with an applied BGO threshold of $E_{\gamma }^{\left(0\right)}⩾2$ MeV. The recoil locus is highlighted by the red dashed lines, which constitute the signal timing gates. (Bottom panel) The separator TOF spectrum with applied MCP-TOF gate and $E_{\gamma }^{\left(0\right)}⩾2$ MeV BGO energy threshold. The background was estimated by taking the average of five sample below the signal region, and five above, each of equal width to the signal gate. The total number of recoils is then given by the total signal, in this case 166 counts, minus a background estimate of 11 counts, which comes to $155{}_{-12}^{+14} {}^{23}\mathrm{Na}$ recoils collected for this yield measurement

Figure 7

(Top panel) MCP TOF vs. separator TOF for the on resonance yield measurement at $E_{\mathrm{c}.\mathrm{m}.}=149$ keV, with an applied BGO threshold of $E_{\gamma }^{\left(0\right)}⩾2.5$ MeV. The recoil locus is highlighted by the red dashed lines, which constitute the signal timing gates. (Bottom panel) The separator TOF spectrum with applied MCP-TOF gate and $E_{\gamma }^{\left(0\right)}⩾2.5$ MeV BGO energy threshold. The background was estimated by taking the average of five sample below the signal region, and five above, each of equal width to the signal gate. The total number of recoils is then given by the total signal, in this case 39 counts, minus a background estimate of 6 counts, which comes to $33{}_{-6}^{+8} {}^{23}\mathrm{Na}$ recoils collected for this yield measurement

Figure 8

Spectrum of highest energy $\gamma$ rays detected by the BGO array $\left(E_{\gamma }^{\left(0\right)}\right)$ in coincidence with a heavy-ion event passing the timing gates for both the MCP-TOF and separator TOF shown in the upper panel in Fig. 7. The red dashed line represents simulated data, scaled to the actual data (blue line). The excess of counts at $2$ MeV, not reproduced in the simulation, are likely being contributed to by random coincidences with background $\gamma$ rays. Therefore, a slightly raised threshold was opted for. Indeed, after performing the separator TOF background subtraction, this threshold choice resulted in a slightly improved statistical error bar compared with a lower 2 MeV threshold used for other yield measurements.

Figure 9

Plot showing the direct capture cross section (a) and astrophysical $S$ factor (b) obtained from various data-sets. The TUNL value re-normalized to the strength of the 458-keV resonance from the present work is also plotted.

Figure 10

Plot showing the LUNA, TUNL and present ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rates as a function of temperature in GK, expressed as a fraction of the STARLIB-2013 rate [58]. The shaded regions represent the $1\sigma$ uncertainty bands associated with each rate.

Figure 11

Predicted surface [Na/Fe] abundance ratio plotted as a function of $S$-process element abundances [$S$/Fe] for a $5M_{\odot }$ ($z=0.006$) AGB star.

Figure 12

Predicted surface [Na/Fe] abundance ratio plotted as a function of $S$-process element abundances [$S$/Fe] for a $2M_{\odot } (z=0.006)$ AGB star.