A New Evaluation of the $${}^{}$$B(p,$$\alpha )\alpha \alpha$$α)αα Reaction Rates

Reaction rates of the \(^{11}\)B(p,\(\alpha\))\(\alpha \alpha\) process have been evaluated on the basis of a data set spanning incident proton energies \(E_p\) from 0.15 to 3.8 MeV. A previously published analysis (Spraker et al. in J Fusion Energy 31(4):357, 2012) of these data provided the number of outgoing \(\alpha\)-particles in a restricted range of the detected \(\alpha\)-energy spectrum, making it unsuitable for the evaluation of the reaction rates. The present work takes advantage of a calculation of the \(\alpha\)-energy spectrum based on a sequential model of the reaction and the assumption that the primary \(\alpha\)-particles are emitted with \(\ell =3\). A full description of this ansatz, which has been shown to reproduce the essential features of the observed \(\alpha\)-energy spectra, can be found in Stave et al. (Phys Lett B 696:26, 2011). The accuracy of these calculated spectra has made it possible to reliably extrapolate the new data to zero-energy \(\alpha\)-particles. In the ensuing calculation of the cross section, the total measured \(\alpha\)-yield is then divided by a fixed factor of three at all incident proton energies. In addition, this technique has enabled a treatment of the \(\alpha _0\) channel where the 12C nuclei decay to the ground state of 8Be via emission of an \(\alpha\)-particle. This channel contributes at incident proton energies above 2 MeV. The new cross section data have then been used to evaluate the \(^{11}\)B(p,\(\alpha\))\(\alpha \alpha\) reaction rates. The new evaluation is \(\sim\)10–15 % higher than the currently accepted result (Angulo et al. in Nucl Phys A 656(1):3, 1999) at temperatures between 200 and 600 keV (2–7 \(\times\) 10\(^9\) K). The inclusion of a narrow, low-lying resonance at \(E_p=0.162\) MeV in the evaluation is found to have a minimal effect on the reaction rate above 100 keV (1.2 \(\times\) 10\(^9\) K), and a higher-lying state at \(E_p=3.75\) MeV is shown to enhance the reaction rates by only \(\sim\)15 % above 400 keV (4.6 \(\times\) 10\(^9\) K).