Energy-dependent effects in coherent pion production

Theoretical calculations have been done for the coherent production of pions in the exclusive reaction 12C + 12 C → 12 C (15.11 MeV) + 12C + π0 at 100 and 250 MeV/nucleon. An analysis is made on how three-body kinematics and other energy dependencies affect the various factors that enter the calculation for the pion differential cross section. Momentum and momentum-transfer diagrams are constructed that show pictorially how projectile- and target-generated pions differ in their intermediate states, even though they lead to the same final states. It is shown how three-body kinematics affect the exchange-process amplitudes that account for projectile- and target-generated pions. Also, the energy dependencies found in the delta width and phase-space factors are assessed as to their relative importance. Momentum robbing and kickback effects to the final-state nuclei from the produced pion are discussed. These effects are shown to give an asymmetry in the pion angular distribution. The study of three-body kinematics and its associated energy dependencies under the Born approximation is considered to be an important first step in the understanding of coherent pion production in heavy-ion collisions, before the complicating features of absorption and distortion are introduced. Even though the pion is much lighter than either of the two equal-mass, final-state nuclei, observable asymmetries are seen in the pion angular distribution that are caused by the produced pion.