The High-Density Symmetry Energy in Heavy-Ion Collisions and Compact Stars

Hermann Wolter

doi:10.3390/universe4060072

Abstract

High-density nuclear symmetry energy is of crucial importance in astrophysics. Information on such energy has been obtained from mass–radius determinations of neutron stars (NSs), and in the future NS mergers will increasingly contribute. In the laboratory, the symmetry energy can be studied in heavy-ion collisions (HICs) at different incident energies over a large range, from very low to several times higher saturation density. Transport theory is necessary to extract the symmetry energy from the typically non-equilibrated nuclear collisions. In this contribution, we first review the transport approaches, their differences, and recent studies of their reliability. We then discuss several prominent observables, which have been used to determine the symmetry energy at high density: collective flow, light cluster emission, and particle production. It is finally argued that the results of the symmetry energy from microscopic many-body calculations, nuclear structure, nuclear reactions, and astrophysics begin to converge but still need considerable improvements in terms of accuracy.

Highlights

The nuclear equation of state (EoS) specifies the energy density of nuclear matter without Coulomb energy as a function of density, temperature, and asymmetry
A second family of transport approaches is the quantum molecular dynamics (QMD) model, in which the evolution of the collision is formulated in terms of the evolution of the coordinates Ri (t) and momenta Pi (t) of the individual nucleons, to as in classical molecular dynamics, but with particles of finite width representing minimum nucleon wave packets, with the width usually assumed to be constant
The results from recent theoretical analyses of the π − /π + ratio using different models of symmetry energies and different program codes are collected in the right panel of Figure 8, while the corresponding symmetry energy density dependencies are shown in the left panel [51,52,53,54]

Summary

Introduction

The nuclear equation of state (EoS) specifies the energy density of nuclear matter without Coulomb energy as a function of density, temperature, and asymmetry. The EoS can be investigated in terrestrial laboratories in HICs. In energetic collisions, densities of up to several times the saturation density can be reached, similar to those that are thought to exist in NSs. In HICs, one has the possibility to scan the density in certain ranges via the incident energy and colliding masses and the asymmetry by the choice of the collision system. Transport descriptions are complex, and the necessary approximations, the implementations, and the accuracy are issues that have to be discussed This contribution aims to review the issues, the problems, and some of the results of the study of high-density symmetry energy with emphasis on HICs. we first discuss the transport theories and give some examples of observables that have been used to constrain the symmetry energies. We summarize the present status of these studies on symmetry energy

Overview of Transport Theories

Fluctuations

Code Comparison

Overview

Collective Flow

Light Cluster Emission

Particle Production

Discussion and Summary