  Recently, the triple-\alpha (3\alpha) process, by which three 4He nuclei are
fused into a 12C nucleus in stars, was studied by different methods in solving
the quantum mechanical three-body problem. Their results of 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 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 12C nucleus. Calculated reaction rate is about 10
times larger than that of the Nuclear Astrophysics Compilation of Reaction
Rates (NACRE) at 10^7 K, and is remarkably smaller than the results of the
recent three-body calculations. We will discuss a possible reason of the
difference.
