First measurement of the low-energy direct capture in ${}^{20}\mathrm{Ne}(p,\gamma ){}^{21}\mathrm{Na}$ and improved energy and strength of the $E_{\text{c.m.}}=368\mathrm{keV}$ resonance

The ${}^{20}\mathrm{Ne}{(p,\gamma )}^{21}\mathrm{Na}$ reaction is the slowest in the NeNa cycle and directly affects the abundances of the Ne and Na isotopes in a variety of astrophysical sites. Here we report the measurement of its direct capture contribution, for the first time below $E_{\mathrm{c}.\mathrm{m}.}=352$ keV, and of the contribution from the $E_{\mathrm{c}.\mathrm{m}.}=368$ keV resonance, which dominates the reaction rate at $T=0.03$–1.00 GK. The experiment was performed deep underground at the Laboratory for Underground Nuclear Astrophysics, using a high-intensity proton beam and a windowless neon gas target. Prompt $\gamma$ rays from the reaction were detected with two high-purity germanium detectors. We obtain a resonance strength $\omega \gamma =(0.112\pm 0.{002}_{\mathrm{stat}}\pm 0.{005}_{\mathrm{sys}})\mathrm{meV}$, with an uncertainty a factor of 3 smaller than previous values. Our revised reaction rate is 20% lower than previously adopted at $T<0.1$ GK and agrees with previous estimates at temperatures $T\ge 0.1$ GK. Initial astrophysical implications are presented.

Figure 1

(a) Level scheme of ${}^{21}\mathrm{Na}$. The transitions from the $E_{\mathrm{c}.\mathrm{m}.}^{}\simeq 366\mathrm{keV}$ resonance are shown in red while the blue arrow indicates the direct capture energy range explored in this work. (b) Gas density profile (black data points) along the beam line through apertures AP2 and AP1 and into the gas chamber. Blue and magenta dash-dotted lines show the detection efficiencies (right $y$ axis) for detectors HPGe90 and HPGe130, respectively, along the beam axis, as a function of distance $z$ from AP2. The efficiency curves refer to the 373-keV $\gamma$ ray emitted by the ${}^{20}\mathrm{Ne}{(p,\gamma )}^{21}\mathrm{Na}$ reaction. (c) Simplified sketch of the experimental setup used for the study of the ${}^{20}\mathrm{Ne}{(p,\gamma )}^{21}\mathrm{Na}$ reaction at LUNA. The beam enters the chamber from the left through the last collimator (AP1) and stops onto a copper calorimeter.

Figure 2

Top panel: Experimental yields for the $E{}_{\gamma }=2425\mathrm{keV}$ as obtained with the HPGe130 (magenta) and HPGe90 (dark blue) detectors as a function of proton beam energy. Bottom panel: Resonance strength determined from experimental yields at each beam energy studied (see text for details).

Figure 3

From top to bottom: LUNA $S$-factor values (red data points) for direct transitions to the second ($2425\mathrm{keV}$), first ($332\mathrm{keV}$), and ground states in ${}^{21}\mathrm{Na}$. Note that the $\mathrm{DC}\to 2425\mathrm{keV}$ transition was analyzed using the secondary $\gamma$ rays ($2425\mathrm{keV}\to \mathrm{GS}$) (see text for details). Error bars for the LUNA data include statistical and systematic uncertainties. The red curve shows our global $R$-matrix fit to the total $S$ factors and includes data by Rolfs et al. [10] (black data points) and by Lyons et al. [11] (blue data points).

Figure 4

LUNA thermonuclear reaction rate for the ${}^{20}\mathrm{Ne}{(p,\gamma )}^{21}\mathrm{Na}$ reaction (red) compared with NACRE [36] (gray), Iliadis et al. [37] (green), and Lyons $etal$. [11] (blue) rates. The shaded area shows the $1\sigma$ uncertainty. The rates are normalized to NACRE. The top $x$ axis shows the Gamow energy for the given temperature range.