Three-Body Calculation of the ⁴He(³H,γ)⁷Li and ⁴He(³He,γ)⁷Be Reactions and Structure of the ⁷Li and ⁷Be at Solar Energies

The two ³H+⁴He and ³He+⁴He fusion reactions at low energies are usually viewed as an approximate external capture process. We study the ⁴He(³H,γ)⁷Li and ⁴He(³He,γ)⁷Be reactions in a cluster model, which can take into account two- and three-body electromagnetic currents, using minimal substitution in the explicit momentum dependence of the two- and three-cluster interactions. Our main goal is to explore how the cross section of the low-energy ³H+⁴He or ³He+⁴He capture reactions depends on energy. The astrophysical S-factors for these reactions are calculated at very low energies. We construct the conserved realistic Argonne v₁₈ for two nucleons and Urbana IX or Tucson-Melbourne three-cluster interactions, which are considered for calculation. We also calculate the binding energies and the structural properties of ³H+⁴He or ³He+⁴He systems. The binding energies are found to be ?37.72 (?36.32) MeV and ?39.35 (?37.43) MeV, with (without) three-body interactions for ⁷Be and ⁷Li, in satisfactory agreement with other theoretical results and experimental data, respectively.