Dissipative collective dynamics and critical points in nuclear matter

Abstract

The shear viscosity $eta$ was calculated for nuclear matter, described as a nucleon system with the van der Waals (vdW) attractive and repulsive interparticle interactions. The collective dynamics was approximated using the collisional Boltzmann kinetic approach. We analytically obtained the results $eta$ in two opposite limits for the Knudsen parameter $omega tau$, where $omega$ is the collective dynamics frequency, and $tau$ is the relaxation time (inverse collision frequency). One of them is the frequent-collision regime (FCR, $omega tau ll 1$ ), and the other is the rare-collision regime (RCR, $omega tau gg 1$). It has been shown, analytically, that the shear viscosity $eta$ depends significantly on the particle-number density $n$ in both regimes, FCR and RCR, mainly due to the attractive interparticle interaction for the FCR, in contrast to the simple Chapman-Enskog results. The remarkable frequency dependence, $eta propto 1/omega^2$ , was found to occur in the RCR analytical calculations. The shear viscosity in units of the entropy density $s$, $eta/s$, was then obtained in the FCR. Accounting for the attractive interaction, one finds that the minimum value of $eta/s$ significantly decreases in the density-temperature ($n-T$) plane, in line with the theoretical and experimental results obtained from heavy ion collision reactions. We also found that the transition from the FCR to the RCR in terms of the Knudsen parameter $omega tau$ takes place at the critical value $omega tau approx 4$.Our results for the sound velocity and attenuation coefficient are in good agreement with experimental data for collective dynamics in several classic gases. We have shown, analytically, that these sound characteristics depend on the specific gas parameters -- particle mass $m$, size of the particle $d$, temperature $T$, and particle-number density $n$ -- through the relaxation time $tau$ in the Knudsen parameter $omega tau$. Therefore, we confirmed the universal scaling properties of the particle gas dynamics, particularly r for nuclear matter. Other critical phenomena in Fermi systems of interacting particles were studied for the liquid-gas phase transition at the static thermodynamic equilibrium. We derived the equation of state in the vdW and Skyrme local density (SLD) approaches accounting for the quantum statistics corrections at first order in the dimensionless quantum statistics parameter $varepsilon approx hbar^3 n(mT)^{-3/2}g^{-1}$, where $m$ and $g$ are the mass and degeneracy factor of the particles respectively, and $T$ is the system temperature. The analytical results for the critical temperature, particle-number density, and pressure were found to be in good agreement with known experimental results, as well as with numerical calculations. For a finite particle-number average, we also analytically obtained the finite maximum of the fluctuations of particle number as a function of the average of the particle-number density near the critical point. Our theoretical description is far away from that to be completed. There are a lot of interesting tasks, which are planned to be solved in the nearest future, as a prolongation of this thesis work. We are going to take into account other transport coefficients, such as the thermal conductivity and diffusion for a more accurate description of the dissipative processes of nuclear matter. A more accurate expression for the particle-number fluctuations will be derived to better explain phenomena such as critical opalescence. In addition, we will develop our approaches by accounting for quantum effects and the asymmetry of nuclear matter. We are focusing on description of the behavior of nuclear matter. However, the results obtained in this work can be used to describe various other systems, apart from an atomic nucleus. It can be applied in different fields of physics, including nuclear physics, high-densed energy physics, physics of electron-ion plasma and nuclear astrophysics.