Dynamics of nuclear fluid. VIII. Time-dependent Hartree-Fock approximation from a classical point of view

In order to facilitate the comparison of the time-dependent Hartree-Fock approximation with other classical theories and to help guide our intuition in understanding the underlying physics, we study the time-dependent Hartree-Fock approximation from a classical viewpoint. We show that the time-dependent Hartree-Fock approximation is approximately equivalent to a purely classical pseudoparticle simulation. In this simulation, a collection of pseudoparticles is introduced to discretize the phase space of spatial and momentum coordinates. The dynamics is completely determined by following the pseudoparticle trajectories which are the same as the trajectories of real particles moving in the self-consistent field. As an application of the concept of the pseudoparticle simulation, we study the origin of the nonfusion events in nearly-head-on heavy-ion collisions as obtained in the time-dependent Hartree-Fock approximation. It is argued that for these nearly-head-on collisions, the emergence of the most energetic pseudonucleons of one nucleus outside the far surface of the other nucleus initiates a coherent flow-through motion because of self-consistency and leads to the breakup of the composite system. Based on this picture, we obtain quantitative estimates of the threshold energies and the low-$l$ fusion window which agree quite well with the time-dependent Hartree-Fock results.