Semiclassical methods are used to analyze the second-order processes—the direct-one step process and the two-step process—in heavy ion collisions. Our main results are the following: (i) In the strong absorption limit, the direct one-step and two-step form factors are equally important and interfere destructively near the grazing angular momentum. The Austern-Blair theory gives satisfactory results for well-matched reactions. The angular distributions of mutual and double excitations are out of phase compared with that of the single excitation. (ii) For the weak to moderate absorption case, the internal part of the two-step process is enhanced. The angular distribution shows the refractive effect of overlapping resonances. Applications have been made to inelastic ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reactions.

• Received 18 October 1983

DOI:https://doi.org/10.1103/PhysRevC.29.811