Reaction mechanism ofLi7(3He,p)9Be andLi7(3H,n)9Be and primordial nucleosynthesis ofBe9

We investigate in a unified way the reaction mechanism of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${(}^3$H,n${)}^9$Be and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${(}^3$He, p${)}^9$Be at the low energies ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≤2 MeV of astrophysical interest. Assuming charge independence of the nuclear reaction amplitudes and taking account of the effects from different isospin contribution, Coulomb interaction, and associated kinematical conditions properly, we constrain the upper and lower bounds of the total cross section of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${(}^3$H,n${)}^9$Be theoretically by using knowledge of the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${(}^3$He, p${)}^9$Be reaction. It is found that the total cross section of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${(}^3$H,n${)}^9$Be at Gamow window energy E∼250 keV is dominated by the near-threshold T=1 resonance whose resonance parameters are not determined at all experimentally, although the direct reaction process makes progressively important contributions at higher energies 500 keV≤${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$. Primordial abundance of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ calculated in the inhomogeneous and standard big-bang models by using the inferred reaction cross section for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${(}^3$H,n${)}^9$Be is compared with recent results of astronomical observations.