Astrophysical $S$ factor and rate of ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ direct capture reaction in a potential model

The astrophysical ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ direct capture process is studied in the framework of a two-body single-channel model with potentials of the Gaussian form. A modified potential is constructed to reproduce the new experimental value of the $S$-wave-scattering length and the known astrophysical $S$ factor at the Gamow energy, extracted from the solar neutrino flux. The resulting potential is consistent with the theory developed by Baye [Phys. Rev. C 62, 065803 (2000)] according to which the $S$-wave scattering length and the astrophysical $S$ factor at zero energy divided by the square of the asymptotic normalization coefficient are related. The obtained results for the astrophysical $S$ factor at intermediate energies are in good agreement with the two data sets of Hammache et al. [Phys. Rev. Lett. 86, 3985 (2001); Phys. Rev. Lett.80, 928 (1998)]. Linear extrapolation to zero energy yields $S_{17}\left(0\right)\approx 20.{51}_{-1.85}^{+2.02}\mathrm{eV}\mathrm{b}$ consistent with the Solar Fusion II estimate. The calculated reaction rates are substantially lower than the results of the NACRE II Collaboration.

Figure 1

Phase shifts in the (a) ${}^{3}S_1$, (b) ${}^{3}P_2$, and (c) ${}^{3}D_2$ partial waves of the $p-{}^7\mathrm{Be}$ scattering state with potentials $V_D$ and $V_M$.

Figure 2

Astrophysical $S$ factors for the ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ synthesis reaction due to the $E1$ transitions (a) ${}^{3}S_1\to {}^{3}P_2$ and (b) ${}^{3}D_2\to {}^{3}P_2$ estimated within the potential models $V_D$ and $V_M$ and their combination.

Figure 3

The partial $E1,E2$, and $M1$ components of the astrophysical $S$ factor for the ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ capture process within the $V_M$ potential model.

Figure 4

Astrophysical $S$ factor for the ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ synthesis reaction within the potential models $V_D$ and $V_M$ in comparison with available experimental data. The shaded area represents the uncertainty corresponding to the potential model $V_M$.

Figure 5

Reaction rates of the direct $p+{}^7\mathrm{Be}\to {}^8\mathrm{B}+\gamma$ capture process within the $V_D$ and $V_M$ potential models normalized to the experimental data by the NACRE Collaboration [2]. The shaded area represents the uncertainty corresponding to the potential model $V_M$.