A generalized Boltzmann equation for nuclear dynamics

We derive a generalized Boltzmann equation from an extended time-dependent mean-field theory, which is self-consistent and incorporates two-body collisions due to the residual interaction. Obtained from a systematic reduction of a more general, but complicated, mean-body theory, this kinetic equation retains many of the quantum effects of the many-body system. Due to proper treatment of quantum causality, its collision integral contains terms which are associated with the principal-value parts of propagators in a quantum-mechanically correct memory kernel. Thus, it properly generalizes the Uehling-Uhlenbeck equation and provides a quantum kinetic theory for nuclear dynamics in both low- and intermediate-energy regions. The new features in this Boltzmann equation are investigated in a nuclear-matter model with a simple effective interaction. We solve for the small-amplitude solutions corresponding to the response of the system to an arbitrary weak external field. The results are contrasted with the collisionless limit and Uehling-Uhlenbeck limit and conclusions are drawn about the dynamical effects of the two-body collisions on the quasiparticles. (orig.)