${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\mathit{\alpha }$,γ${)}^{16}$O reaction in a multiconfiguration microscopic model

The E1 and E2 components of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(α,γ${)\mathrm{}}^{16}$O S factor are investigated microscopically with a generator-coordinate calculation involving α${+\mathrm{}}^{12}$${\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$, α${+\mathrm{}}^{12}$C($2_1^{+}$), p${+\mathrm{}}^{15}$${\mathrm{N}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$, and n${+\mathrm{}}^{15}$${\mathrm{O}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ configurations. The theoretical capture cross sections towards the ground state and excited states are in semiquantitative agreement with experiment. Simple corrections to the microscopic expressions lead to good agreement with experimental data. The corrected model provides an S factor of 0.24 MeV b at the astrophysically important energy 0.3 MeV.