Detailed study of the astrophysical direct capture reaction ${}^6\mathrm{L}\mathrm{i}(p,\gamma {)}^7\mathrm{B}\mathrm{e}$ in a potential model approach

The astrophysical $S$ factor and reaction rates of the direct capture process ${}^6$Li(p,$\gamma {)}^7$Be are estimated within a two-body single-channel potential model approach. Central potentials of the Gaussian-form in the ${}^2{P}_{3\mathrm{/}2}$ and ${}^2{P}_{1\mathrm{/}2}$ waves are adjusted to reproduce the binding energies and the empirical values of the asymptotic normalization coefficients (ANC) for the ${}^7$Be(3/2${}^{-}$) ground and ${}^7$Be(1/2${}^{-}$) excited bound states, respectively. The parameters of the potential in the most important ${}^2{S}_{1\mathrm{/}2}$ scattering channel were fitted to reproduce the empirical phase shifts from the literature and the low-energy astrophysical $S$ factor of the LUNA collaboration. The obtained results for the astrophysical $S$ factor and the reaction rates are in a very good agreement with available experimental data sets. The numerical estimates reproduce not only the absolute values, but also the energy and temperature dependence of the $S$ factor and reaction rates of the LUNA collaboration, respectively. The estimated ${}^7\mathrm{L}\mathrm{i}\mathrm{/}\mathrm{H}$ primordial abundance ratio $(4.67\pm 0.04)\times {10}^{-10}$ is well consistent with recent BBN result of $(4.72\pm 0.72)\times {10}^{-10}$ after the Planck observation.