Pion production in a transport model based on mean fields from chiral effective field theory

Abstract

We develop a Boltzmann-Uehling-Uhlenbeck (BUU) transport model based on the $\mathrm{Sk}\ensuremath{\chi}{\mathrm{m}}^{*}$ energy density functional, which is constructed from fitting the nuclear equation of state and nucleon effective masses in asymmetric nuclear matter predicted by the two- and three-body chiral interactions as well as the binding energies of finite nuclei. This new $\ensuremath{\chi}\mathrm{BUU}$ transport model is then used to study how baryon mean-field potentials affect the kinematics of a scattering or decay process and the equilibrium properties of a hot $N\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}\text{\ensuremath{-}}\ensuremath{\pi}$ system in a box with periodic boundary conditions. We find that the inclusion of mean-field potentials in the energy conservation condition for scattering and decay processes is necessary to maintain the equilibrium numbers of $N,\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}$, and $\ensuremath{\pi}$. Although the baryon mean-field potentials have significant effects on the total $\mathrm{\ensuremath{\Delta}}$ and $\ensuremath{\pi}$ numbers, they only slightly affect the ratio of effective negatively to positively charged pions. We also study pion production in central $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ collisions at the incident energy of $E/A=400$ MeV and compare the results with the experimental data from the Four Pi (FOPI) Collaboration at the Gesellschaft f\ur Schwerionenforschung mbH (GSI) in Germany. We find that our model can well describe the experimental results and the threshold effect due to baryon mean-field potentials does not affect much the charged pion ratio in this model. We further make predictions on pion production for the ongoing experiments of $^{132}\mathrm{Sn}+^{124}\mathrm{Sn}$ and $^{108}\mathrm{Sn}+^{112}\mathrm{Sn}$ at the incident energy of $E/A=270$ MeV by the SAMURAI Pion-Reconstruction and Ion-Tracker ($\mathrm{S}\ensuremath{\pi}\mathrm{RIT}$) Collaboration at the Institute of Physical and Chemical Research (RIKEN) in Japan.