Study of the $^7Be(p,γ)^8B$ and $^7Li(n,γ)^8Li$ capture reactions using the shell model embedded in the continuum

We apply the realistic shell model which includes the coupling between many-particle (quasi-)bound states and the continuum of one-particle scattering states to the spectroscopy of mirror nuclei: $^8$B and $^8$Li, as well as to the description of low energy cross sections (the astrophysical S factors) in the capture reactions:$^7Be(p,\gamma)^8B$ and $^7Li(n,\gamma)^8Li$.