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 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 ^ { 12 } C 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 .