Boltzmann equations and hydrodynamics for nuclear systems

Abstract

The Keldysh-Schwinger formalism for causal Green's functions gives an-in principle-self-contained coupled system of (functional) equations for transport processes, which is used for the microscopic investigation of nuclear non-equilibrium systems. First, the general statistical equations are obtained by means of the energy moments of the GF-equations. The essential quantity is the causal mass operator (effective single-particle) potential, which determines the generalized densities. The transition to nuclear physics is achieved by assuming a weak energy dependence of the mass operator. With this simplification one obtains — as desired — a generalization of the time-dependent Hartree-Fock-approach, in which the single-particle propagation is determined by the real part of the total microscopic optical potential. The damping is caused by the imaginary part of the optical potential, where two-particle collisions and excitations contribute. The Vlasov-Uehling-Uhlenbeck-equation — recently applied in nuclear physics — is a special approximation, in which for the single-particle description only the Hartree-term enters. The dissipation term is simplified by approximating the ladder approximation via the optical theorem. Nuclear hydrodynamics emerges by means of the momentum-moments of the Wigner transformed statistical equations. Collision contributions — in the ladder approximation — in the “Navier-Stokes” equations demand at least the inclusion of second order moments. Furthermore one can derive equations for macroscopic variables. As example we give the equation of motion for the centre-of-mass coordinate for two colliding nuclei.