Astrophysical S factor and rate of ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ direct capture reaction in a potential model

Abstract

The astrophysical ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ direct capture process is studied in the framework of a two-body single-channel model with potentials of the Gaussian form. A modified potential is constructed to reproduce the new experimental value of the $S$-wave scattering length and the known astrophysical $S$ factor at the Gamow energy, extracted from the solar neutrino flux. The resulting potential is consistent with the theory developed by Baye [Phys. Rev. C {\bf 62} (2000) 065803] according to which the $S$-wave scattering length and the astrophysical $S$ factor at zero energy divided by the square of ANC are related. The obtained results for the astrophysical $S$ factor at intermediate energies are in good agreement with the two data sets of Hammache {\it et al.} [Phys. Rev. Lett. {\bf 86}, 3985 (2001); {\it ibid.} {\bf 80}, 928 (1998)]. Linear extrapolation to zero energy yields $S_{17}(0)\approx (20.5\pm 0.5)\mathrm{eV}\mathrm{b}$, consistent with the Solar Fusion II estimate. The calculated reaction rates are substantially lower than the results of the NACRE II collaboration.

arXiv comment16 pages, 5 figures, 2 tables

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• Ab initio informed evaluation of the radiative capture of protons on ${}^7$Be
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• Study of the direct ${}^{16}\mathrm{O}(p,\gamma {)}^{17}\mathrm{F}$ astrophysical capture reaction within a potential model approach
• Nuclear Reactions in Evolving Stars