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

TL;DR

This study models the $^7$Be(p, γ)$^8$B reaction using a potential model to accurately predict the astrophysical S factor and reaction rates, aligning with experimental data and solar neutrino observations.

Contribution

A modified potential model is developed to reproduce experimental scattering lengths and S factors, providing improved predictions for the reaction rate of $^7$Be(p, γ)$^8$B.

Findings

Predicted S factor at zero energy: ~20.5 eV b.

Reaction rates are lower than NACRE II estimates.

Results agree with experimental data and solar neutrino flux.

Abstract

The astrophysical $^7{\rm Be}(p, \gamma)^8{\rm B}$ 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) \, \rm eV \, b $, consistent with the Solar Fusion II estimate. The calculated reaction rates are substantially lower than the results of the NACRE II collaboration.