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 $19.0^{+4.0}_{-1.0}$ eV.b.
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