Impacts of momentum dependent interaction, symmetry energy and near-threshold $NN\to N\Delta$ cross sections on isospin sensitive flow and pion observables

TL;DR

This study uses the UrQMD model to analyze how momentum dependence, symmetry energy, and near-threshold NN to NΔ cross sections influence isospin-sensitive flow and pion observables, constraining symmetry energy at specific densities.

Contribution

It provides updated model parameters and characteristic densities to accurately describe isospin-sensitive observables and constrains symmetry energy at relevant densities.

Findings

Flow characteristic density around 1.2 times nuclear saturation density

Pion characteristic density around 1.5 times nuclear saturation density

Constraints on symmetry energy: S(1.2ρ₀)=34±4 MeV, S(1.5ρ₀)=36±8 MeV

Abstract

Based on the ultra-relativistic quantum molecular dynamics (UrQMD) model, the impacts of momentum dependent interaction, symmetry energy and near-threshold $NN\to N\Delta$ cross sections on isospin sensitive collective flow and pion observables are investigated. Our results confirm that the elliptic flow of neutrons and charged particles, i.e. $v_2^n$ and $v_2^{ch}$, are sensitive to the strength of momentum dependence interaction and the elliptic flow ratio, i.e., $v_2^n/v_2^{ch}$, is sensitive to the stiffness of symmetry energy. For describing the pion multiplicity near the threshold energy, accurate $NN\to N\Delta$ cross sections are crucial. With the updated momentum dependent interaction and $NN\to N\Delta$ cross sections in UrQMD model, seven observables, such as directed flow and elliptic flow of neutrons and charged particles, the elliptic flow ratio of neutrons to charged particles, charged pion multiplicity and its ratio $\pi^-/\pi^+$, can be well described by the parameter sets with the slope of symmetry energy from 5 MeV to 70 MeV. To describe the constraints of symmetry energy at the densities probed by the collective flow and pion observables, the named characteristic density is investigated and used. Our analysis found that the flow characteristic density is around 1.2$\rho_0$ and pion characteristic density is around 1.5$\rho_0$, and we got the constrains of symmetry energy at characteristic densities are $S(1.2\rho_0)=34\pm 4$ MeV and $S(1.5\rho_0)=36\pm 8$ MeV. These results are consistent with previous analysis by using pion and flow observable with different transport models, and demonstrate a reasonable description of symmetry energy constraint should be presented at the characteristic density of isospin sensitive observables.