Brent Barker

Towards a nonequilibrium Green’s function description of nuclear reactions: One-dimensional mean-field dynamics

Nonequilibrium Green’s function methods allow for an intrinsically consistent description of the evolution of quantal many-body body systems, with inclusion of different types of correlations. In this paper, we focus on the practical developments needed to build a Green’s function methodology for nuclear reactions. We start out by considering symmetric collisions of slabs in one dimension within the mean-field approximation. We concentrate on two issues of importance for actual reaction simulations. First, the preparation of the initial state within the same methodology as for the reaction dynamics is demonstrated by an adiabatic switching on of the mean-field interaction, which leads to the mean-field ground state. Second, the importance of the Green’s function matrix-elements far away from the spatial diagonal is analyzed by a suitable suppression process that does not significantly affect the evolution of the elements close to the diagonal. The relative lack of importance of the far-away elements is tied to system expansion. We also examine the evolution of the Wigner function and verify quantitatively that erasing of the off-diagonal elements corresponds to averaging out of the momentum–space details in the Wigner function.

From Stopping to Viscosity in Nuclear Reactions

Data on stopping in intermediate‐energy central heavy‐ion collisions are analyzed following transport theory based on the Boltzmann equation. In consequence, values of nuclear shear viscosity are inferred. The inferred values are significantly larger than obtained for free nucleon dispersion relations and free nucleon‐nucleon cross sections.

Towards a nonequilibrium Green's function description of nuclear reactions

Semiclassical time-dependent approaches are nowadays able to describe energetic central collisions of heavy isotopes with minimal assumptions. Simulations in the mean-field picture have provided insight on both nuclear structure and low-energy many-body reaction mechanisms. In this context, nonequilibrium Greens functions techniques have the potential to improve the description of the time evolution of nuclear systems by introducing effects beyond the mean-field. We describe a first attempt to use the Kadanoff-Baym dynamics for one-dimensional nuclear systems, with a particular emphasis on the process of correlation buildup.

Towards Quantum Transport for Central Nuclear Reactions

Nonequilibrium Greens functions represent a promising tool for describing central nuclear reactions. Even at the single-particle level, though, the Greens functions contain more information that computers may handle in the foreseeable future. In this study, we explore slab collisions in one dimension, first in the mean field approximation and demonstrate that only function elements close to the diagonal in arguments are relevant, in practice, for the reaction calculations. This bodes well for the application of the Greens functions to the reactions. Moreover we demonstrate that an initial state for a reaction calculation may be generated through adiabatic transformation of interactions. Finally, we report on our progress in incorporating correlations into the dynamic calculations.

Towards quantum transport for nuclear reactions

Nonequilibrium Greens functions represent a promising tool for describing central nuclear reactions. Even at the single-particle level, though, Greens functions contain more information that computers may handle in the foreseeable future. In this study, we investigate whether all the information contained in Greens functions is necessarily relevant when describing the time evolution of nuclear reactions. For this, we carry out mean-field calculations of slab collisions in one dimension.

From Stopping to Viscosity in Heavy Ion Collisions

Stopping in heavy ion collisions is investigated with the aim of learning about the shear viscosity of nuclear matter. Boltzmann equation simulations are compared to available data on stopping in the energy range of 20–117 MeV/nucleon. Stopping observables used include momentum anisotropy and linear momentum transfer. The data show that modeling the transport with free nucleon‐nucleon cross‐sections is inaccurate and reduced cross‐sections are required. Reduction of the cross‐sections produces an increase in the shear viscosity of nuclear matter, compared to calculations based on free cross‐sections.

Time‐Dependent Green’s Functions Description of One‐Dimensional Nuclear Mean‐Field Dynamics

The time‐dependent Green’s functions formalism provides a consistent description of the time evolution of quantum many‐body systems, either in the mean‐field approximation or in more sophisticated correlated approaches. We describe an attempt to apply this formalism to the mean‐field dynamics of symmetric reactions for one‐dimensional nuclear slabs. We pay particular attention to the off‐diagonal elements of the Green’s functions in real space representation. Their importance is quantified by means of an elimination scheme based on a super‐operator cut‐off field and their relevance for the global time evolution is assessed. The Wigner function and its structure in the mean‐field approximation is also discussed.