The astrophysical S factor of the ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ radiative capture reaction is analyzed at zero energy in a simplified potential model where the scattering wave function and its energy derivative at zero energy are replaced by their asymptotic expressions. A positive (negative) scattering length in the initial s wave reduces (increases) the value of $S\left(0\right).$ The ratio $S^{\prime }\mathrm{}\left(0\right)/S\left(0\right)\mathrm{}$ is much more sensitive to the scattering length than $S\left(0\right).$ The effective range of the initial wave is found to play a negligible role. Existing models suggest a negative value for the scattering length, but not large enough to lead to important corrections.

• Received 27 July 2000

DOI:https://doi.org/10.1103/PhysRevC.62.065803