Structure of the 8 B and 8 Li nuclei and the astrophysical S 17(0) -factor of the 7 Be(p, gamma) 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+ cubed He(cubed H)+ p(n) three-body potential cluster model based on the hyperspherical Lagrange-mesh method. The two-body realistic potentials have been applied from the literature. Convergent theoretical estimates for the three-body binding energy and matter radius have been obtained with the maximal hypermomentum K max=22 and 28 for the ground and excited 1+ states, respectively. The ANC value of the virtual transition of the 8 B nucleus is estimated self-consistently by matching the overlap integral of the 8 B three-body and the 7 Be two-body wave functions with it's asymptotics. The obtained values are 0.211 fm-1/2 and 0.739 fm-1/2 in the spin 1 and spin 2 channels, respectively. For the ANC values of the 8 Li nucleus the estimates 0.220 fm-1/2 and 0.774 fm-1/2 are extracted. The ratio C 2(8 B)/C 2(8 Li)=0.912 implies a breaking of the mirror symmetry of the strong nuclear forces of order 27% due to the Coulomb interaction and the dynamical three-body effects. For the S 17(0) -factor an estimate 22.492 plus or minus0.014 eV b was obtained based on the asymptotic theory developed by D. Baye [Phys. Rev. C 62,065803 (2000)]. The spin 2 channel contributes with S(2) 17(0)=20.838 plus or minus 0.014 eV b, while the spin 1 channel yields S(1) 17(0)=1.654 plus or minus 0.003 eV b. These results for S 17(0) are in a good agreement with the estimate 20.8 plus or minus0.7 (th) plus or minus1.4 (exp) eV b of the SF II, but larger than the recommended value 20.5 plus or minus0.70 eV b of the SF III. At the same time, our estimate is very close to the value 22.4 eV b used in the most successful Solar Model BAR2M [W. Yang and Z. Tian, AJ 970 (2024), 38].