Microscopic theory of theBe8(α,γ)12C reaction in a three-cluster model

The generator-coordinate method is applied to the study of the three-α-particle system. The choice of the basis functions allows us to calculate the α${+\mathrm{}}^8$Be phase shifts. We perform a comparison between the full three-cluster approach and two of its approximations. Distortion effects are shown to be important in the spectroscopic properties of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. We present the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$(α,γ${)\mathrm{}}^{12}$C S factor derived in the three-α-particle model. At low temperatures, the reaction rate is found to be slightly different from earlier studies.