  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.
