Origins of the energy distribution structure in coherent pion production at intermediate energies

New calculations have been done that now cover the intermediate energy range from 100 MeV/nucleon to 2.0 GeV/nucleon incident energy for the reaction 12C + 12C -12C + 12C (15.11 MeV) +p0, where constructive, coherent D-hole states are excited in either nucleus while the companion nucleus is excited to a coherent nucleon-hole state describing the spin-isospin, giant resonant state at 15.11 MeV. The D (1232 MeV) isobar then decays to a nucleon and pion. Theoretical pion energy distributions are calculated and, for the first time, results above 400 MeV/nucleon are shown. A theoretical basis for understanding how the shapes of the pion distributions change as a function of incident energy is described. The fundamental shape of the D-production amplitude as a function of momentum transfer is discussed and the effects of the energy-dependent nuclear width are examined. Furthermore, the connection between the origins of the pion distribution to the final pion shapes is made and the importance of the giant resonance in providing an important signature is pointed out. By pushing the calculations above 400 MeV/nucleon, it was discovered that sliding kinematics and kinematic turnarounds occur due to the two-to-three-body sequential nature of the reactions and these effects determine the final structure of the pion distributions at higher incident energies.