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

The astrophysical $S$ factor and reaction rates of the direct capture process ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ 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 ${}^7\mathrm{Be}(3/2^{-})$ ground and ${}^7\mathrm{Be}(1/2^{-})$ 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 $(4.67\pm 0.04)\times {10}^{-10}$ is consistent with recent big bang nucleosynthesis result of $(4.72\pm 0.72)\times {10}^{-10}$ after the Planck telescope observation.

Figure 1

Phase shift in the ${}^{2}S_{1/2}$ partial wave of the $p{\text{−}}^6\mathrm{Li}$ scattering state within the potential model $V_M$. The experimental phase shifts are taken from Ref. [38].

Figure 2

The contributions of the $E1$ transition operator to the astrophysical $S$ factor within the $V_M$ potential model from different initial scattering states to the final ${}^7\mathrm{Be}(3/2^{-})$ ground state.

Figure 3

Effect of the SUSY transformation of the $S$-wave potential on the $E1$ astrophysical $S$ factor within the potential model $V_M$.

Figure 4

The partial contributions of the $E2$ and $M1$ transition operators to the astrophysical $S$ factor from different initial scattering states to the final ${}^7\mathrm{Be}(3/2^{-})$ ground state within the $V_M$ potential model.

Figure 5

Contributions of the $E1, E2$, and $M1$ transition operators to the astrophysical $S$ factor from different initial scattering states to the final ${}^7\mathrm{Be}(1/2^{-})$ excited bound state within the $V_M$ potential model.

Figure 6

Contributions of $E1, E2$, and $M1$ transition operators to the astrophysical $S$ factor of the ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ synthesis process, calculated within the potential model $V_M$.

Figure 7

Astrophysical $S$ factor of the radiative direct capture ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ reaction, calculated with the potential $V_M$ in comparison with the experimental data from Refs. [21, 23, 25, 49].

Figure 8

Comparison of the calculated reaction rates in present potential model for the direct ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ capture process with the results of Refs. [25, 26], normalized to the NACRE rate. The shaded area presents the error bar of the LUNA data [22].