Four-body calculation of ¹²C(α, γ)¹⁶O radiative capture reaction at stellar energies

On the basis of the four-alphamodel, the ¹²C(α, γ)¹⁶Oradiative capture process is investigated by using the four-body Faddeev–Yakubovsky equations as well as the two- and three-body electromagnetic currents. The present calculation is an application of our current conservation realistic potentials method for the ¹²C(α, γ)¹⁶Oradiative capture process. This work clears the way formore refinedmodels of radiative capture based on two- and three-body realistic potentials and current conservation. The calculation is carried out by considering the ⁴He + ¹²C (1 + 3) and the ⁸Be + ⁸Be (2 + 2) subamplitudes, respectively. Radiative capture ¹²C(α, γ)¹⁶Oreaction is one of the most important reactions in nuclear astrophysics. For this reaction, the electric dipole transitions between states with the same isospin are forbidden in the first order. Because the state 1⁺ and 0⁺ ground state nuclei ¹⁶O have zero isospin, thus the electric dipole radiations are not at the first order between two levels and electric dipole radiation will be the second order and electric dipole radiation is the same order as the electric quadrupole radiation. Therefore, we must consider the effects of both radiations. In comparison with other theoretical methods and available experimental data, good agreement is achieved for the E₁ and E₂ contribution to the cross section and the astrophysical S factor for this process.