Structure of ${}^{8}B$ and astrophysical $S_{17}$ factor in Skyrme Hartree-Fock theory

Abstract

We investigate the ground state structure of ${}^8$B within the Skyrme Hartree-Fock framework where spin-orbit part of the effective interaction is adjusted to reproduce the one-proton separation energy of this nucleus. Using same set of force parameters, binding energies and root mean square radii of other light p-shell unstable nuclei, ${}^8$Li, ${}^7$B,${}^7$Be, and ${}^9$C, have been calculated where a good agreement with corresponding experimental data is obtained. The overlap integral of ${}^8$B and ${}^7$Be wave functions has been used to determine the root mean square radius of the single proton in a particular orbit and also the astrophysical S factor ($S_{17}$) for the ${}^7$Be($p,\gamma {)}^8$B radiative capture reaction. It is found that the asymptotic region (distances beyond 4 fm) of the p-shell single proton wave function contributes more than half to the calculated value (4.93 fm) of the corresponding single particle root mean square radius. We determine a $S_{17}$ 21.1 eV.b which is in good agreement with the recommended value for near zero energy $S_{17}$ of $19.0_{-1.0}^{+4.0}$ eV.b.

Comments: some typos corrected