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The astrophysical $^7{\rm Be}(p, \gamma)^8{\rm B}$ direct capture process isstudied in the framework of a two-body single-channel model with potentials ofthe Gaussian form. A modified potential is constructed to reproduce the newexperimental value of the $S$-wave scattering length and the knownastrophysical $S$ factor at the Gamow energy, extracted from the solar neutrinoflux. The resulting potential is consistent with the theory developed by Baye[Phys. Rev. C {\bf 62} (2000) 065803] according to which the $S$-wavescattering length and the astrophysical $S$ factor at zero energy divided bythe 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 ofHammache {\it et al.} [Phys. Rev. Lett. {\bf 86}, 3985 (2001); {\it ibid.} {\bf80}, 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 ratesare substantially lower than the results of the NACRE II collaboration.

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