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

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.