Detailed study of the astrophysical direct capture reaction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>6</mml:mn></mml:mmultiscripts><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo><mml:mmultiscripts><mml:mi>Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> in a potential model approach

The astrophysical $S$ factor and reaction rates of the direct capture process $^{6}\mathrm{Li}(p,\ensuremath{\gamma})^{7}\mathrm{Be}$ are estimated within a two-body single-channel potential model approach. Nuclear potentials of the Gaussian form in the $^{2}P_{3/2}$ and $^{2}P_{1/2}$ waves are adjusted to reproduce the binding energies and the empirical values of the asymptotic normalization coefficients (ANC) for the $^{7}\mathrm{Be}(3/{2}^{\ensuremath{-}})$ ground and $^{7}\mathrm{Be}(1/{2}^{\ensuremath{-}})$ excited bound states, respectively. The parameters of the potential in the most important $^{2}S_{1/2}$ 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 very good agreement with available experimental data sets. The numerical estimates reproduce not only the absolute values, but also the energy dependence of the $S$ factor and the temperature dependence of the reaction rates of the LUNA Collaboration. The estimated $^{7}\mathrm{Li}/\mathrm{H}$ primordial abundance ratio of $(4.67\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ is consistent with recent big bang nucleosynthesis result of $(4.72\ifmmode\pm\else\textpm\fi{}0.72)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ after the Planck telescope observation.

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