Nuclear slabs with Green’s functions: mean field and short-range correlations

Abstract

Computational difficulties aside, nonequilibrium Green’s functions appear ideally suited for investigating the dynamics of central nuclear reactions. Many particles actively participate in those reactions. At the two energy extremes for the collisions, the limiting cases of the Green’s function approach have been successful: the time-dependent Hartree–Fock theory at low energy and Boltzmann equation at high. The strategy for computational adaptation of the Green’s function to central reactions is discussed. The strategy involves, in particular, incremental progression from one to three dimensions to develop and assess approximations, discarding of far-away function elements, use of effective interactions and preparation of initial states for the reactions through adiabatic switching. At this stage we concentrate on inclusion of correlations in one dimension, where relatively few approximations are needed, and we carry out reference calculations that can benchmark approximations needed for more dimensions. We switch on short-range interactions generating the correlations adiabatically in the Kadanoff–Baym equations to arrive at correlated ground states for uniform matter. As the energy of the correlated matter does not quite match the expectations for nuclear matter, we add mean field to arrive at the match in energy. From there on, we move to finite systems. In switching on the correlations, we observe emergence of extended tails in momentum distributions and evolution of single particle occupations away from 1 to 0.