Low-energy ${}^7$Li($n,\gamma$)${}^8$Li and ${}^7$Be($p,\gamma$)${}^8$B radiative capture reactions within the Skyrme Hartree-Fock approach

The electromagnetic dipole transitions in ${}^7$Be($p,\gamma$)${}^8$B and ${}^7$Li($n,\gamma$)${}^8$Li reactions at the keV-energy region were analyzed simultaneously within the Skyrme Hartree-Fock potential model. The Skyrme Hartree-Fock calculation is adopted as a microscopic approach to obtain consistently the single-particle bound and scattering states in the calculation of the radial overlap function within the potential model. All non-resonant and resonant electromagnetic dipole transitions are taken into account. The electric dipole transitions are successfully described with the slightest adjustment. The resonant magnetic dipole transitions at $633$ keV and $2184$ keV of ${}^7$Be($p,\gamma$)${}^8$B reaction, and the one at $222$ keV of ${}^7$Li($n,\gamma$)${}^8$Li are also analyzed. The astrophysical ${\mathcal{S}}_{17}(0)$ factor of ${}^7$Be($p,\gamma$)${}^8$B reaction is found to be $22.3$ eV,b.