We present a complete systematics (excitation functions and system-size dependences) of global stopping and sideflow for heavy ion reactions in the energy range between 0.09A GeV and 1.93A GeV. For the heaviest system, Au+Au, we observe a plateau of maximal stopping extending from about 0.2A to 0.8A GeV with a fast drop on both sides. The degree of stopping, which is shown to remain significantly below the expectations of a full stopping scenario, is found to be highly correlated to the amount of sideflow.

Nuclear stopping from 0.09A GeV to 1.93A GeV and its correlation to flow

Properties of the nuclear equation of state (EoS) can be probed by measuring the dynamical properties of nucleus-nucleus collisions. In this study, we present the directed flow (v1), elliptic flow (v2) and stopping (VarXZ) measured in fixed target Sn + Sn collisions at with the SπRIT Time Projection Chamber. We perform Bayesian analyses in which EoS parameters are varied simultaneously within the Improved Quantum Molecular Dynamics-Skyrme (ImQMD-Sky) transport code to obtain a multivariate correlated constraint. The varied parameters include symmetry energy, S0, and slope of the symmetry energy, L, at saturation density, isoscalar effective mass, ⁎ms⁎/mN, isovector effective mass, ⁎mv⁎/mN and the in-medium cross-section enhancement factor η. We find that the flow and VarXZ observables are sensitive to the splitting of proton and neutron effective masses and the in-medium cross-section. Comparisons of ImQMD-Sky predictions to the SπRIT data suggest a narrow range of preferred values for ⁎ms⁎/mN, ⁎mv⁎/mN and η. 

Constraining nucleon effective masses with flow and stopping observables from the SπRIT experiment

Initial fluctuation is one of the ingredients that washes fingerprints of the nuclear symmetry energy on observables in heavy-ion collisions. By artificially using the same initial nuclei in all collision events, the effect of the initial fluctuation on isospin-sensitive observables, e.g., the yield ratio of free neutrons with respect to protons Nn/Np, 3H/3He yield ratio, the yield ratio between charged pions π−/π+, and the elliptic flow ratio or difference between free neutrons and protons v2n/v2p (v2n-v2p), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy Elab = 400 MeV/nucleon are calculated. It is found that the effect of the initialization on the yields of free protons and neutrons is small, while for the yield of pions, the directed and elliptic flows are found to be apparently influenced by the choice of initialization because of the strong memory effects. Regarding the isospin-sensitive observables, the effect of the initialization on Nn/Np and 3H/3He is negligible, while π−/π+ and v2n/v2p (v2n-v2p) display a distinct difference among different initializations. The fingerprints of symmetry energy on π−/π+ and v2n/v2p can be either enhanced or reduced when different initializations are utilized.

Quantifying the Effect of Initial Fluctuations on Isospin-Sensitive Observables from Heavy-Ion Collisions at Intermediate Energies

The momentum dependence of the nucleon mean-field potential in a wide momentum range can be an important factor to determine the $\mathrm{\ensuremath{\Delta}}$ resonance and pion production in intermediate-energy heavy-ion collisions. In particular, in neutron-rich systems such as $^{132}\mathrm{Sn}+^{124}\mathrm{Sn}$ collisions, we need to carefully treat the momentum dependence because the neutron and proton potentials can have different momentum dependence, as characterized at low momenta by effective masses. In the present work, we rigorously calculate the collision terms of $NN\ensuremath{\leftrightarrow}N\mathrm{\ensuremath{\Delta}}$ and $\mathrm{\ensuremath{\Delta}}\ensuremath{\leftrightarrow}N\ensuremath{\pi}$ processes with the precise conservation of energy and momentum under the presence of momentum-dependent potentials for the initial and final particles of the process. The potentials affect not only the threshold condition for the process but also the cross section in general as a function of the momenta of the initial particles, which is treated in a natural way in the present work. Calculations are performed by combining the nucleon dynamics obtained by the antisymmetrized molecular dynamics (AMD) model with a newly developed transport code which we call sJAM. The calculated results for central $^{132}\mathrm{Sn}+^{124}\mathrm{Sn}$ collisions at 270 MeV/nucleon clearly show that the momentum dependence of the neutron and proton potentials has a significant impact on the $NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}$ process, and this information is strongly reflected in the charged pion ratio (${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$). We also investigate the effects of the high-density symmetry energy and the isovector part of the potential of $\mathrm{\ensuremath{\Delta}}$ resonances on pion production, which we find are relatively small compared to the effect of the momentum dependence of the neutron and proton potentials. 

Collision integral with momentum-dependent potentials and its impact on pion production in heavy-ion collisions

In this work, we propose a novel method for calculating the occupation probability in the Pauli blocking of the quantum molecular dynamics type models. This method refines the description of the Pauli blocking ratio in the nuclear matter and that in the finite nucleus. The influence of the new Pauli blocking method on the heavy ion collisions observables, such as the charge distribution, the free neutron to proton yield ratios, and the extracted physical quantities, such as the in-medium nucleon-nucleon cross sections, are investigated. For the extracted in-medium nucleon-nucleon cross sections, our results show that it will be enhanced 1.1$-$2.5 times than that with the conventional Pauli blocking method at the beam energy less than 150 MeV/u, which highlights the importance of a refined Pauli blocking method for developing an advanced transport model to describe complex heavy ion collisions.

Novel Pauli blocking method in quantum molecular dynamics type models

Rapidity distributions of Z = 1 isotopes and the nuclear symmetry energy from Sn+Sn collisions with radioactive beams at 270 MeV/nucleon

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Rapidity distributions of Z = 1 isotopes and the nuclear symmetry energy from Sn+Sn collisions with radioactive beams at 270 MeV/nucleon