[Paper Review] Systematics of azimuthal asymmetries in heavy ion collisions in the 1 A GeV regime

FOPI Collaboration, W. Reisdorf+52 more|arXiv (Cornell University)|Dec 14, 2011

High-Energy Particle Collisions Research3 references4 citations

TL;DR

This study presents a systematic analysis of directed and elliptic flow in heavy-ion collisions across 25 nuclear systems at 1 A GeV, using the FOPI detector at GSI. It finds that a stiff nuclear equation of state is incompatible with data, while evidence for enhanced neutron repulsion in asymmetric nuclear matter is observed, particularly in mass-3 clusters like ³He and ³H.

ABSTRACT

Using the large acceptance apparatus FOPI, we study central and semi-central collisions in the reactions (energies in A GeV are given in parentheses): 40Ca+40Ca (0.4, 0.6, 0.8, 1.0, 1.5, 1.93), 58Ni+58Ni (0.15, 0.25, 0.4), 96Ru+96Ru (0.4, 1.0, 1.5), 96Zr+96Zr (0.4, 1.0, 1.5), 129Xe+CsI (0.15, 0.25, 0.4), 197Au+197Au (0.09, 0.12, 0.15, 0.25, 0.4, 0.6, 0.8, 1.0, 1.2, 1.5). The observables include directed and elliptic flow. The data are compared to earlier data where possible and to transport model simulations. A stiff nuclear equation of state is found to be incompatible with the data. Evidence for extra-repulsion of neutrons in compressed asymmetric matter is found.

Motivation & Objective

• To establish a comprehensive systematics of directed and elliptic flow for light charged particles in central and semi-central heavy-ion collisions at 1 A GeV.
• To probe the nuclear equation of state (EoS) and isospin-dependent effects in compressed nuclear matter using flow observables.
• To test the consistency of transport models with experimental data across a broad range of systems and energies.
• To investigate isospin-dependent forces, particularly enhanced neutron repulsion, in asymmetric nuclear matter.
• To provide stringent constraints on theoretical models by comparing flow data with simulations across multiple collision systems and energies.

Proposed method

• Measured directed ($v_1$) and elliptic ($v_2$) flow of identified light charged particles (p, d, ³He, ³H) in 25 heavy-ion systems across 0.09–1.93 A GeV.
• Used the FOPI large-acceptance spectrometer at GSI to detect particles with high efficiency and momentum resolution.
• Applied event-by-event analysis with centrality selection via impact parameter ($b_0$) to isolate flow contributions.
• Corrected raw flow parameters using detector-specific correction factors ($d_i$, $e_i$) derived from Monte Carlo simulations.
• Compared experimental flow data with transport model simulations (e.g., BUU, QMD) to test EoS and isospin effects.
• Analyzed rapidity dependence of $v_2(y_0)$ to assess EoS sensitivity beyond mid-rapidity.

Experimental results

Research questions

• RQ1 How do directed and elliptic flow of light charged particles vary across different nuclear systems and beam energies in the 1 A GeV regime?
• RQ2 What constraints do flow data place on the stiffness of the nuclear equation of state in compressed nuclear matter?
• RQ3 Is there experimental evidence for enhanced neutron repulsion in isospin-asymmetric nuclear matter?
• RQ4 How well do transport models reproduce the observed flow patterns, especially in mass-3 clusters?
• RQ5 Can the rapidity dependence of elliptic flow provide additional sensitivity to the EoS and isospin effects?

Key findings

• A stiff nuclear equation of state is ruled out by the data, as it fails to reproduce the observed flow patterns across all systems.
• Evidence for extra repulsion of neutrons in asymmetric nuclear matter is found, particularly in the $v_2(y_0)$ behavior of ³He and ³H, which show consistent differences over the full rapidity range.
• Directed flow data for mass-3 clusters are consistent with enhanced neutron repulsion, supporting the isospin-dependent force hypothesis.
• The $v_2(y_0)$ shape for ³He and ³H is best described by models incorporating stronger neutron-neutron repulsion than neutron-proton or proton-proton interactions.
• The data show that flow observables at 1 A GeV are sensitive to isospin effects, even at moderate densities, and provide a new probe of nuclear incompressibility.
• Correction factors for flow extraction were systematically derived and applied, improving the reliability of the extracted $v_1$ and $v_2$ values across 10 centrality bins.