Resonating-Group Calculation of Radiative Capture Reactionsα(He3,γ)Be7andα(t,γ)Li7at Astrophysical Low Energies

Total cross sections and astrophysical $S$ factors of the radiative capture reactions $\alpha ({}_{}{}^3{}_{}{}^{}\mathrm{He},\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ and $\alpha (t,\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Li}$ are investigated by the resonating-group method. The theoretical value of the $S$ factor at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=10\mathrm{}$ keV is predicted to be 0.508 keV·b without the use of any artificial parameters. An interesting difference between the mirror reactions is found and theoretically explained.