Numerical simulation of medium energy heavy ion reactions.

Abstract

Reactions between heavy ions at medium energy are calculated using the Boltzmann-Uehling- Uhlenbeck equation. This equation incorporates the effects of a mean field as well as Pauli b)ocking of the nucleon-nucleon collisions. The numerical solution for two light systems, ' O+' C at 253 MeV bombarding energy and ' C+' C at 844 MeV bombarding energy, is presented and discussed in detail. In tne absence of nucleon-nucleon collisions, the theory reduces to classical mean-field physics and agrees well with the quantal time-dependent Hartree-Pock theory. With collisions, the system is driven toward equilibrium even at the lower bombarding energy. The final state nucleon distribution is compared to single-particle spectra and is found-to agree quite well in shape. The study of collisions between heavy ions at medium energy is a subject which is still poorly understood. At low energy, the time-dependent Hartree-Fock (TDHF) theory' provides a powerful tool for describing single- particle observables. At high energies, nucleon-nucleon collisions dominate the dynamics, and the intranuclear cascade (INC) models are applicable. ' Unfortunately, the approximations in these methods are not valid in the medium energy regime. Hartree-Fock theory requires that the residual interaction be neglected in comparison to the mean field generated by the nucleons. At low energy the residual interactions have small effects because of Pauli blocking. However, at medium energy the available phase space is enlarged and the residua1 interactions are important, producing collisions between the nucleons. Attempts have been made to include a collision term in TDHF calculations in order to extend the range of appli- cability to higher energies. Due to the enormous mathematical complexity, these calculations have not yet produced useful results for interpretation of the experi- mental data. It should also be mentioned that the repre- sentation of quantum corrections to the mean-field theory by a collision integral may not even be well justified under the conditions found in medium-energy nucleus-nucleus collisions. In deriving a collision integral, one must as- sume that the time scale for the mean-field evolution is long compared with the time scale of the collisions. How- ever, a more general approach without the collision ap- proximation gives a theory which is even more difficult to solve numerically. Despite the theoretical uncertainties, we feel it is worthwhile to make further approximations in order to arrive at a computationally feasible theory. It appears that a manageable description from a computational point of view is obtained from a classical treatment of the single-particle density in the quantum transport equation. First numerical results were obtained by the Michigan State University group. ' The