Memory and correlation effects in nuclear collisions

Relaxation rates are calculated by numerically solving the Kadanoff-Baym equations for an extended system of nuclear matter. The time evolutions of initial nonequilibrium distributions in momentum space, defined by two Fermi spheres, is studied. Comparisons are made with the (semi-) classical method used in BUU, VUU, etc. Danielewicz has found that at a nucleon density of ∼0.3 nucleon/fm³ and an equilibrated temperature of about 70 MeV, the quantum relaxation rate is smaller than the classical by a factor of about 2. These results are confirmed. The calculations are extended to lower temperatures (energies) and densities and this ratio is found to be essentially unchanged over a wide range although there are deviations from this rule as seen in the text. The quantum evolutions are started either with an uncorrelated or a correlated initial distribution. The latter are obtained with imaginary time stepping. The relaxation time approximation was previously found to be excellent for the classical evolution. It is found to be as good for the quantum evolution. The memory time is in the present calculations found to be less than 5 fm/c (i.e., ∼1.7×10^-23 s). One concludes that quantum-mechanical effects have to be incorporated in the models of heavy ion collisions and nuclear dynamics. Not until this is done comprehensively will one be able to readily assess the role of two-nucleon collisions in the equilibration process.