Eur. Phys. J. A (2018) 54: 40
https://doi.org/10.1140/epja/i2018-12470-1

Regular Article - Theoretical Physics

Feasibility of constraining the curvature parameter of the symmetry energy using elliptic flow data

Department of Theoretical Physics, IFIN-HH, Reactorului 30, 077125, Măgurele/Bucharest, Romania

^* e-mail: dan.cozma@theory.nipne.ro

Received: 20 July 2017
Accepted: 25 January 2018
Published online: 9 March 2018

Abstract

A QMD transport model that employs a modified momentum dependent interaction (MDI2) potential, supplemented by a phase-space coalescence model fitted to FOPI experimental multiplicities of free nucleons and light clusters is used to study the density dependence of the symmetry energy above the saturation point by a comparison with experimental elliptic flow ratios measured by the FOPI-LAND and ASYEOS Collaborations in ¹⁹⁷Au + ¹⁹⁷Au collisions at 400 MeV/nucleon impact energy. A previous calculation using the same model has proven that neutron-to-proton and neutron-to-charged-particles elliptic flow ratios probe on average different densities allowing in principle the extraction of both the slope L and curvature parameters of the symmetry energy. To make use of this result a Gogny interaction inspired potential is modified by the addition of a density dependent, momentum independent term, while enforcing a close description of the empirical nucleon optical potential, allowing independent modifications of L and K_sym. Comparing theoretical predictions with experimental data for neutron-to-proton and neutron-to-charged-particles elliptic flow ratios the following constraint is extracted: MeV and MeV. Theoretical errors include effects due to uncertainties in the isoscalar part of the equation of state, value of the isovector neutron-proton effective mass splitting, in-medium effects on the elastic nucleon-nucleon cross-sections, Pauli blocking algorithm variants and scenario considered for the conservation of the total energy of the system. Systematical uncertainties are generated by the inability of the transport model to reproduce experimental light-cluster-to-proton multiplicity ratios. A value for L free of systematical theoretical uncertainties can be extracted from the neutron-to-proton elliptic flow ratio alone: MeV. It is demonstrated that elliptic flow ratios reach a maximum sensitivity on the parameter in heavy-ion collisions of about 250 MeV/nucleon impact energy, allowing a reduction of its experimental component of uncertainty to about 150 MeV.