Structure of B 8 and astrophysical S 17 factor in Skyrme Hartree-Fock theory

We investigate the ground-state structure of $^{8}\mathrm{B}$ 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 $^{8}\mathrm{Li}$, $^{7}\mathrm{B}$, $^{7}\mathrm{Be}$, and $^{9}\mathrm{C}$ have been calculated, where a good agreement with corresponding experimental data is obtained. The overlap integral of $^{8}\mathrm{B}$ and $^{7}\mathrm{Be}$ 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 $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$ radiative capture reaction. It is found that the asymptotic region (distances beyond $4\phantom{\rule{0.3em}{0ex}}\text{fm}$) of the $p$-shell single-proton wave function contributes more than half to the calculated value $(4.76\phantom{\rule{0.3em}{0ex}}\text{fm})$ of the corresponding single-particle root mean square radius. The value of ${S}_{17}$ is determined to be $22.0\phantom{\rule{0.3em}{0ex}}\text{eV}\phantom{\rule{0.3em}{0ex}}\mathrm{b}$ which is in good agreement with the recommended value for the near zero energy ${S}_{17}$ of ${19.1}_{\ensuremath{-}1.0}^{+4.0}\phantom{\rule{0.3em}{0ex}}\text{eV}\phantom{\rule{0.3em}{0ex}}\mathrm{b}$.