${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ Reaction Rate at Astrophysically Relevant Energies

The production of ${}^{26}\mathrm{Al}$ in massive stars is sensitive to the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ cross section. Recent experimental data suggest the currently recommended cross sections are underestimated by a factor of $\sim 40$. We present here differential cross sections for the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ reaction measured in the energy range $E_{\mathrm{c}.\mathrm{m}.}=1.7–2.5\mathrm{MeV}$. Concurrent measurements of Rutherford scattering provide absolute normalizations that are independent of variations in target properties. Angular distributions are measured for both $p_0$ and $p_1$ permitting the determination of total cross sections. The results show no significant deviation from the statistical model calculations upon which the recommended rates are based. We therefore retain the previous recommendation without the increase in cross section and resulting stellar reaction rates by a factor of 40, impacting the ${}^{26}\mathrm{Al}$ yield from massive stars by more than a factor of 3.

Figure 1

A schematic of the experimental setup within the scattering chamber. The incoming ${}^4\mathrm{He}$ beam is indicated by the arrow. The NaCl target was orientated at 45° relative to the beam axis. Two double-sided silicon strip detectors were used to detect outgoing protons and $\alpha$ particles, see the text for details. For clarity both front- and back-side segmentation of the detectors are shown.

Figure 2

(a) The measured angular distribution of elastically scattered alpha particles from ${}^{23}\mathrm{Na}$ at a beam energy of 2.94 MeV. The solid line is the distribution expected for pure Rutherford scattering. (b) The stoichiometric ratio of Na and Cl in the target foil, as determined by Rutherford scattering, as a function of the integrated beam impinging on the foil.

Figure 3

Representative energy spectra from the annular DSSD ($S3$) and the quadratic DSSD plus the pad detector telescope ($W1$). In the latter case a coincidence between the two detectors is required to remove the background due to $\alpha$ particles stopping in the quadratic DSSD. The effective center of mass energy in each case is given in the plot, see the text for details. The small peak at * has an energy consistent with the $p_0$ transition in ${}^{19}\mathrm{F}(\alpha ,p){}^{22}\mathrm{Ne}$, and may therefore be indicative of a thin layer of ${}^{19}\mathrm{F}$ on the target surface, see the text for further discussion.

Figure 4

Proton angular distributions from the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ reaction. The energies given are the effective center of mass energies, corrected for the target thickness. For the lowest energy $p_1$ data shown reliable differential cross sections could only be obtained in the annular DSSD detector, located at backward angles in the laboratory frame. The dotted lines show fits of Legendre polynomials to the data.

Figure 5

Cross sections for the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ reaction. The energies given are effective energies, corrected for energy losses within the target. See the text for details. For comparison cross sections from the statistical model code Non-Smoker [14] and the measurement reported in Ref. [6] are also shown.

Figure 6

The single-resonance contribution to the total rate obtained from Non-Smoker calculations based upon the measured strength of the resonance at $E_{\mathrm{c}.\mathrm{m}.}=2.14\mathrm{MeV}$ (see text for details).