Structure of the $^8$B and $^8$Li nuclei and the astrophysical $S_{17}(0)$-factor of the $^7$Be($p,γ$)$^8$B direct capture process within a three-body model

The structure of the ground $(2^+)$ and excited $(1^+)$ bound states of the $^8$B and $^8$Li nuclei is studied within the framework of the $α+^3$He($^3$H)+$p(n)$ three-body potential cluster model based on the hyperspherical Lagrange-mesh method. The two-body realistic potentials have been applied f