Recently, the triple-$\alpha$ (3$\alpha$) process, by which three ${}^4$He nuclei are fused into a ${}^{12}$C nucleus in stars, was studied by using different methods to solve the quantum mechanical three-body problem. The results for the thermonuclear reaction rate for the process differ by several orders at low stellar temperatures of ${10}^7–{10}^8$ K. In this paper, we will present calculations of the 3$\alpha$ process by using a modified Faddeev three-body formalism in which the long-range effects of Coulomb interactions are accommodated. The reaction rate of the process is calculated via an inverse process: three-alpha (3-$\alpha$) photodisintegration of a ${}^{12}$C nucleus. The calculated reaction rate is about 10 times larger than that of the Nuclear Astrophysics Compilation of Reaction Rates at ${10}^7$ K and is notably smaller than the results of recent three-body calculations. We will discuss a possible reason for the difference.

• Received 16 December 2012

DOI:https://doi.org/10.1103/PhysRevC.87.055804