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,a)aa 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 a-particles in a restricted range of the detected aenergy spectrum, making it unsuitable for the evaluation of the reaction rates. The present work takes advantage of a calculation of the a-energy spectrum based on a sequential model of the reaction and the assumption that the primary a-particles are emitted with ' ¼ 3. A full description of this ansatz, which has been shown to reproduce the essential features of the observed a-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 a-particles. In the ensuing calculation of the cross section, the total measured a-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 a 0 channel where the 12 C nuclei decay to the ground state of 8 Be via emission of an aparticle. 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,a)aa reaction rates. The new evaluation is $ 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 Â 10 9 K). The inclusion of a narrow, low-lying resonance at E p ¼ 0:162 MeV in the evaluation is found to have a minimal effect on the reaction rate above 100 keV (1.2 Â 10 9 K), and a higher-lying state at E p ¼ 3:75 MeV is shown to enhance the reaction rates by only $ 15 % above 400 keV (4.6 Â 10 9 K).

First experimental proof of Proton Boron Capture Therapy (PBCT) to enhance protontherapy effectiveness

“…According to the most recent studies and interpretations, p +  11 B —> 3α can be described as a two-step reaction (involving 12 C and 8 Be nuclei excitation) with a main resonance occurring at a 675 keV (center of mass energy) and where the maximum cross section of 1.2 barn is measured 38,39 . A more detailed description of the reaction is reported in Methods .…”

Enhancement of Radiation Effectiveness in Proton Therapy: Comparison Between Fusion and Fission Methods and Further Approaches

“…have been presented in literature. The Sikora & Weller 46 reported cross-sections for low energy incoming protons from 600 keV up to 4 MeV and the TENDL 2017 47 for energy more than 4 MeV. Accordingly, the above expression has been re-written as follow;…”

High-current stream of energetic α particles from laser-driven proton-boron fusion

“…In such reaction, predominant at energies below 10 MeV [2][3][4][5][6][7], the final product is the generation of three energetic α particles. Several theoretical and experimental studies report a main resonance peak occurring at 675 keV proton energy in the lab, with a maximum cross section of 1.2 barn [8,9] [ Fig. 1(a)].…”