Thermodynamic and Transport properties of hot asymmetric nuclear matter within a chiral SU(3) model

TL;DR

This paper investigates the thermodynamic and transport properties of hot asymmetric nuclear matter using a chiral SU(3) model to capture in-medium modifications of nucleons. The authors solve for the mean-field values of the scalar and vector fields to obtain density- and temperature-dependent effective masses $m_i^*$ and chemical potentials $\mu_i^*$, then compute the shear viscosity $\eta$ and thermal conductivity $\kappa$ via the Boltzmann equation in the relaxation time approximation with a momentum-averaged $\tau_i$. Key findings show that in-medium effects reduce $\eta$ but enhance $\kappa$ compared to a free gas, and that the ratio $\eta/s$ decreases with density, particularly at higher temperatures; isospin asymmetry raises both $\eta/s$ and $\kappa$, with a pronounced impact on $\kappa$ at high density. The results have implications for interpreting collective flow and hadron spectra in compressed baryonic matter experiments such as CBM at FAIR.

Abstract

We investigate the thermodynamic and transport properties in hot nuclear matter accounting for the medium modifications of the nucleons within a chiral SU(3) model including effects from isospin asymmetry. Using the relaxation time approximation, the transport coefficients of the shear viscosity and thermal conductivity are studied. The shear viscosity, $η$, calculated within the chiral SU(3) model is observed to be smaller than the values calculated for free nucleon gas, whereas the thermal conductivity $κ$ is appreciably larger as compared to the free nucleon gas. The shear viscosity coefficient to entropy density ratio, $η/s$, drops with increasing baryon density which becomes more pronounced at higher temperatures in the chiral SU(3) model as compared to the case of a free nucleon gas. The effect due to isospin asymmetry on the coefficient of shear viscosity turns out to be marginal. However, in the chiral SU(3) model, in presence of isospin asymmetry, the coefficient of thermal conductivity has an appreciably higher value as compared to the one for symmetric nuclear matter. The present study of the thermodynamic as well as transport properties in hot nuclear matter is of relevance for relativistic heavy-ion collisions with different initial isospin asymmetry, in particular for the compressed baryonic matter (CBM) experiment at the FAIR facility at GSI.

Figures (10)

• Figure 1: Pressure, p (in MeV/fm$^3$) is plotted as a funciton of $\rho_B/\rho_0$, the baryon density in units of nuclear matter saturation density, for different values of temperature, for isospin symmetric ($\eta_N$=0) and asymmetric nuclear matter (with asymmetry parameter, $\eta_N$=0.3). The effects due to the medium modified nucleons calculated using the chiral SU(3) model (shown in subplot (b)) are compared with the case of free nucleon gas (shown in subplot (a)).
• Figure 2: Energy density (in MeV/fm$^3$) is plotted as a funciton of $\rho_B/\rho_0$, the baryon density in units of nuclear matter saturation density, for different values of temperature, for isospin symmetric ($\eta_N$=0) and asymmetric nuclear matter (with asymmetry parameter, $\eta_N$=0.3). The effects due to the medium modified nucleons calculated using the chiral SU(3) model (shown in subplot (b)) are compared with the case of free nucleon gas (shown in subplot (a)).
• Figure 3: Entropy density, $s$ (in fm$^{-3}$), is plotted as a funciton of $\rho_B/\rho_0$, the baryon density in units of nuclear matter saturation density, for different values of temperature, for isospin symmetric ($\eta_N$=0) and asymmetric nuclear matter (with asymmetry parameter, $\eta_N$=0.3). The effects due to the medium modified nucleons calculated using the chiral SU(3) model (shown in subplot (b)) are compared with the case of free nucleon gas (shown in subplot (a)).
• Figure 4: $C_s^2$ is plotted as a funciton of $\rho_B/\rho_0$, the baryon density in units of nuclear matter saturation density, for different values of temperature, for isospin symmetric ($\eta_N$=0) and asymmetric nuclear matter (with asymmetry parameter, $\eta_N$=0.3). The effects due to the medium modified nucleons calculated using the chiral SU(3) model (shown in subplot (b)) are compared with the case of free nucleon gas (shown in subplot (a)).
• Figure 5: Entropy per baryon, $S/B$, is plotted as a funciton of $\rho_B/\rho_0$, the baryon density in units of nuclear matter saturation density, for different values of temperature, for isospin symmetric ($\eta_N$=0) and asymmetric nuclear matter (with asymmetry parameter, $\eta_N$=0.3). The effects due to the medium modified nucleons calculated using the chiral SU(3) model (shown in subplot (b)) are compared with the case of free nucleon gas (shown in subplot (a)).