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 $\left(S_{17}\right)$ for the ${}^7\mathrm{Be}\left(p,\gamma \right){}^8\mathrm{B}$ radiative capture reaction. It is found that the asymptotic region (distances beyond $4\text{fm}$) of the $p$-shell single-proton wave function contributes more than half to the calculated value $\left(4.76\text{fm}\right)$ of the corresponding single-particle root mean square radius. The value of $S_{17}$ is determined to be $22.0\text{eV}\mathrm{b}$ which is in good agreement with the recommended value for the near zero energy $S_{17}$ of ${19.1}_{-1.0}^{+4.0}\text{eV}\mathrm{b}$.

• Received 20 June 2003

DOI:https://doi.org/10.1103/PhysRevC.68.054320