One step production of 6 alpha particles of {sup 12}C + {sup 12}C {r_arrow} 6 {sup 4}He

According to the Born approximation, the cross section for {sup 12}C + {sup 12}C{r_arrow} 6 {sup 4}He is proportional to p(p {sup n}){vert_bar}{l_angle}{Psi}{sub f}{vert_bar}V{vert_bar}{Psi}{sub i}{r_angle}{vert_bar}{sup 2} in which n = 14 is the number of independent parameters, and V is the potential acting between {alpha}clusters in the beam with the {alpha} clusters in the target. {Psi}{sub f} is the final state with each cluster expressed as a plane wave. {Psi}{sub i} is the initial state consisting of {alpha} cluster {sup 12}C wave functions times plane waves for the relative motion. The phase space factor, p, is slowly varying. The matrix element, {l_angle}{Psi}{sub f}{vert_bar}V{vert_bar}{Psi}{sub i}{r_angle}, is large if the momentum of one or more clusters are spectators which have the same momentum after, as before the reaction. If two{alpha} particles in the target and two in the beam are spectators, the threshold for the reaction is 88 Mev, and the sum of the energies of the two remaining {alpha} particles is 1/3 of the beam energy less about 14 Mev binding energy. Such peaks in the sum of the energies of two {alpha} particles have been observed for {sup 12}C energies from 660 to 1860 Mev.