A New Evaluation of the $${}^{11}$$ 11 B(p, $$\alpha )\alpha \alpha$$ α ) α α Reaction Rates

Abstract

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).