The Effects of One-Body Dissipation and Collective Inertias in Heavy Ions Scattering and Fusion

A classical dynamical model of heavy ion scattering and fusion is presented. The model includes deformations, deformation-dependent inertias and one-body friction in both the entrance and exit channels. The deformation-dependent inertias are calculated using a hydrodynamic approach and the one-body friction is determined with the classical wall friction formalism. This model is used to study the effects of one-body friction and collective inertias on strongly damped heavy ion reactions and fusion. Quantum -mechanical calculations suggest that the strength of classical one-body friction, as calculated by the wall formalism, is too large by a factor of 3. Therefore, the fusion excitation functions for the reactions: ^{16} O + ^{16}O, ^{28}Si + ^{28 }Si, ^{40}Ca + ^{40}Ca and ^{56}Fe + ^{56 }Fe are calculated and compared with similar calculations in which the strength of the wall friction has been reduced by a factor of 3. Calculations using the full wall friction reproduce the experimental fusion excitation functions more accurately than calculations using the weaker wall friction. Also, because hydrodynamical inertias are the smallest possible classical inertias, the fusion excitation functions for: ^{16 }O + ^{16}O, ^{28}Si + ^ {28}Si, ^{40} Ca + ^{40}Ca and ^{56}Fe + ^ {56}Fe are calculated with the size of the collective inertias increased by a factor of 2 over the hydrodynamical values. Once again, calculations using hydrodynamical collective inertias reproduce the experimental fusion excitation functions more accurately than calculations using the larger collective inertias. The effects of one -body friction and collective inertias on heavy ion scattering are also investigated; reaction times, scattering angles and energy loss are determined as functions of energy and angular momentum for the reactions ^{98 }Mo + ^{98}Mo and ^{238}U + ^{238}U. These reactions are also studied with the strength of the wall friction decreased by a factor of 3 and with the magnitude of the inertias increased by a factor of 2. These calculations reveal that it may be possible to separate the effects of one -body friction from the effects of collective inertias in heavy ion reactions by measuring both fusion cross sections and energy losses. Trajectory calculations also reveal that inelastic scattering reactions are overdamped only for near central collisions. Thus, a rigorous treatment of deformation dependent collective inertias and entrance channel deformations is necessary.