Experimental study of the astrophysically important ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ and ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reactions

The ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ and ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reactions are important for our understanding of the ${}^{26}\mathrm{Al}$ abundance in massive stars. The aim of this work is to report on a direct and simultaneous measurement of these astrophysically important reactions using an active target system. The reactions were investigated in inverse kinematics using ${}^4\mathrm{He}$ as the active target gas in the detector. We measured the excitation functions in the energy range of about 2 to 6 MeV in the center of mass. We have found that the cross sections of the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ and the ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reactions are in good agreement with previous experiments and with statistical-model calculations. The astrophysical reaction rate of the ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reaction has been reevaluated and it was found to be larger than the recommended rate.

Figure 1

Energy-loss signals measured in the 18 strips of the MUSIC detector for events of the ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ (blue), ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ (red), and ${}^{23}\mathrm{Na}(\alpha ,{\alpha }^{\prime }){}^{23}\mathrm{Na}$ (gray) reactions occurring in strip 4. The black lines originate from the ${}^{23}\mathrm{Na}$ beam.

Figure 2

Two-dimensional plot of $\mathrm{\Delta }E$ values for events occurring in strip 4, averaged over five (${\text{Av}}_5$) and four strips (${\text{Av}}_4$) in order to improve the separation of events from the ${}^{23}\mathrm{Na}(\alpha ,{\alpha }^{\prime }){}^{23}\mathrm{Na}$, the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$, and the ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reactions.

Figure 3

Excitation functions of the ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ (blue) and the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ (red) reactions measured with the MUSIC detector for beam energies of 51.5 and 57.4 MeV, labeled as low energy and high energy, respectively.

Figure 4

Excitation functions of the ${}^{23}\mathrm{Na}(\alpha ,p){}^{26}\mathrm{Mg}$ reaction obtained in this work (red solid circles), in comparison with the results from Almaraz-Calderon et al. [9] (blue triangles), Tomlinson et al. [7] (green open circles), Howard et al. [8] (magenta diamonds), and the statistical-model calculations from Mohr [19].

Figure 5

Excitation functions of the ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reaction obtained in this work (blue squares), by Norman et al. [10] (small magenta circles) with their energy-averaged values (large maroon circles), and by Skelton et al. [11] (small light green diamonds) with their energy-averaged values (large dark green diamonds). For Doukellis and Rapaport [12] only the energy-averaged values (large red triangles) are shown. The dashed line represents the statistical-model calculations by Mohr [19].

Figure 6

The ${}^{23}\mathrm{Na}(\alpha ,n){}^{26}\mathrm{Al}$ reaction rate calculated in this work (dash-dotted line), in the NACRE compilation (dashed line) [13], and by Caughlan and Fowler [25] (dotted line). The grey area represents the error band.