Evolutions of in-medium baryon-baryon scattering cross sections and stiffness of dense nuclear matter from Bayesian analyses of FOPI proton flow excitation functions

TL;DR

This study uses Bayesian analysis with a Gaussian Process emulator to infer in-medium baryon-baryon scattering cross sections and the stiffness of dense nuclear matter from FOPI proton flow data, revealing a transition from soft to stiff equations of state with increasing beam energy.

Contribution

First application of Bayesian inference with Gaussian Process emulators to analyze in-medium baryon interactions and nuclear matter stiffness from heavy-ion collision data.

Findings

The in-medium baryon-baryon scattering cross section modification factor increases from 0.7 to 1.0 with beam energy.

The nuclear matter stiffness parameter K transitions from around 220 MeV to 320 MeV as beam energy increases.

Evidence of a gradual transition from soft to stiff nuclear matter in heavy-ion collisions.

Abstract

Within a Bayesian statistical framework using a Gaussian Process (GP) emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions with momentum-independent Skyrme interactions, we infer from the proton directed and elliptical flow in mid-central Au+Au reactions at beam energies from 150 to 1200 MeV/nucleon taken by the FOPI Collaboration the posterior Probability Distribution Functions (PDFs) of the in-medium baryon-baryon scattering cross section (BBSCS) modification factor $X$ (with respect to their free-space values) and the stiffness parameter $K$ of dense nuclear matter. We find that the most probable value of $X$ evolves from around 0.7 to 1.0 as the beam energy $E_{beam}/A$ increases. On the other hand, the posterior PDF($K$) may have dual peaks having roughly the same height or extended shoulders at high $K$ values. More quantitatively, the posterior PDF($K$) changes from having a major peak around 220 MeV characterizing a soft EOS in the reaction at $E_{beam}/A$=150 MeV to one that peaks around 320 MeV indicating a stiff EOS in the reactions at $E_{beam}/A$ higher than about 600 MeV. The transition from soft to stiff happens in mid-central Au+Au reactions at beam energies around 250 MeV/nucleon in which $K=220$ MeV and $K=320$ MeV are approximately equally probable. Altogether, the FOPI proton flow excitation function data indicate a gradual hardening of hot and dense nuclear matter as its density and temperature increase in reactions with higher beam energies.