Quantum Dynamics of Nuclear Slabs: Mean Field and Short-Range Correlations

TL;DR

This paper explores the application of nonequilibrium Green's functions to nuclear reaction dynamics, focusing on including correlations in one-dimensional models and benchmarking approximations for higher dimensions.

Contribution

It introduces a strategy for adapting Green's function methods to nuclear reactions, including correlation effects in 1D and benchmarking for future multi-dimensional studies.

Findings

Correlations cause extended tails in momentum distributions.

Single particle occupations evolve away from 0 and 1.

Benchmark calculations for correlated ground states in 1D.

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 and 0.