[Paper Review] Symmetry energy at high densities from neutron/proton flow excitation functions

P. Russotto, A. Le Fèvre+10 more|arXiv (Cornell University)|May 19, 2021

Gamma-ray bursts and supernovae4 citations

TL;DR

This paper proposes a beam-time campaign at GSI/FAIR to constrain the density dependence of the nuclear symmetry energy up to 2ρ₀ using neutron/proton elliptic flow excitation functions in 197Au+197Au collisions at 250–1000 AMeV. By measuring neutron, proton, and isotopically resolved light cluster flows with advanced detectors like NeuLAND, KRAB, and FARCOS, the study aims to tightly constrain the symmetry energy slope parameter L and curvature parameter K_sym, providing critical input for neutron star modeling and nuclear transport theories.

ABSTRACT

Determination of the high density behavior of the symmetry energy through the simultaneous measurement of elliptic flow excitation functions of neutrons, protons and light clusters is proposed. The elliptic flow developed in relativistic heavy ion collisions has been proven theoretically and experimentally to have a unique sensitivity and robustness in probing the symmetry energy up to around $2 ρ_{o}$. The knowledge of the density dependence of the symmetry energy in a broad range of densities will provide a missing link for astrophysical predictions of the neutron star mass--radius relation. In particular, the data colud provide tighter constraints on the slope parameter L and entirely new limits on $K_{sym}$, the currently poorly constrained symmetry energy curvature parameter.

Motivation & Objective

• To determine the high-density behavior of the symmetry energy up to 2ρ₀ using elliptic flow excitation functions in relativistic heavy-ion collisions.
• To provide tighter constraints on the symmetry energy slope parameter L and new, previously weakly constrained limits on the curvature parameter K_sym.
• To test and refine nuclear transport models by measuring correlations among neutron, proton, and light cluster emissions.
• To complement astrophysical observations from X-ray telescopes and gravitational wave detectors with high-precision experimental data on dense nuclear matter.
• To commission and utilize new detector systems (KRAB, FARCOS, NeuLAND) for improved resolution and data quality in high-density nuclear matter studies.

Proposed method

• Measure elliptic flow excitation functions of neutrons, protons, and isotopically resolved light clusters (d, ³He, ³H) in central 197Au+197Au collisions at 250, 400, 600, and 1000 AMeV.
• Utilize the NeuLAND detector for high-resolution neutron and proton spectroscopy, enabling access to densities up to ~30% higher than with elemental resolution.
• Employ the KRAB plastic scintillator barrel to provide multiplicity-based centrality triggers and high-resolution reaction plane reconstruction for θ > 30°.
• Use the R3B New Time-of-Flight Wall (TOFD) and START detector for event-by-event centrality and reaction plane determination at forward and backward angles.
• Apply the FARCOS array for high-angular-resolution particle-particle correlation functions and interferometric characterization of emission sources.
• Use KRATTA triple telescopes for precise identification of light charged particles at mid-rapidity, ensuring clean separation of isotopes without punch-through.

Experimental results

Research questions

• RQ1 How does the elliptic flow ratio of neutrons to protons vary with beam energy and density, and what does it reveal about the symmetry energy at high densities?
• RQ2 What are the constraints on the symmetry energy slope parameter L and curvature parameter K_sym derived from the measured flow excitation functions?
• RQ3 How do correlations between neutron, proton, and light cluster emissions depend on the density dependence of the symmetry energy?
• RQ4 To what extent do transport models with stiff vs. soft symmetry energy parametrizations reproduce the observed flow trends across the energy range?
• RQ5 How do isotopic compositions and yields of light clusters inform the thermodynamic properties and emission dynamics of hot nuclear sources?

Key findings

• The 400 AMeV energy point is identified as optimal for reference measurements due to maximum squeeze-out and clean particle identification in NeuLAND.
• The 250 AMeV energy is predicted to offer the highest sensitivity to the symmetry energy curvature parameter K_sym, based on model calculations.
• The 600 AMeV energy is predicted to maximize sensitivity to the symmetry energy slope parameter L, providing a key constraint on the E_sym(ρ) behavior.
• The 1000 AMeV energy allows access to the highest densities, where the neutron/proton elliptic flow ratio retains ~15% sensitivity to E_sym parametrization, enabling high-density constraints.
• The KRAB detector is expected to reduce background from delta-electrons by a factor of ~30 via a helium sleeve, significantly improving data quality over previous experiments.
• The combination of NeuLAND, KRAB, FARCOS, and KRATTA is expected to provide unprecedented resolution in particle identification and flow measurements, enabling robust extraction of L and K_sym.