Liquid-gas phase transition of nuclear matter

TL;DR

This work surveys evidence for a first-order liquid-gas phase transition in nuclear matter and its mapping to a Van der Waals-like equation of state. It combines multifragmentation data with thermodynamic corrections to extract a critical point at $T_c\approx 18$ MeV, $P_c\approx0.3$ MeV fm$^{-3}$, and $n_c\approx n_0/3$, and interprets these results through virial expansions and schematic two-body potentials. The review then covers thermal Hartree-Fock and variational calculations, which reproduce the LGT and yield mean-field critical exponents, followed by chiral EFT approaches (in-medium ChPT and FRG) that provide consistent predictions for symmetric and neutron-rich matter. Finally, the paper places the LGT in the QCD phase diagram, discusses the isospin dependence and chemical freeze-out, and highlights the role of pionic fluctuations and chiral dynamics in shaping the transition, emphasizing its separation from chiral restoration and deconfinement regions.

Abstract

A survey is presented summarizing the empirical evidence for and interpretations of a first-order liquid-gas phase transition in nuclear matter. Earlier developments and the present state of knowledge about the extraction of the critical point for such a transition, primarily from the systematics of multifragmention data, are outlined. By analogy with a Van der Waals equation of state, the empirically deduced critical temperature and pressure permit to draw a schematic picture of the underlying nuclear potential. More detailed approaches to the liquid-gas transition using self-consistent nuclear Hartree-Fock and variational calculations are described. Critical exponents are reported. Then chiral effective field theory, as the low-energy realization of QCD, is discussed in the context of nuclear thermodynamics. Its implications for the liquid-gas transition in symmetric nuclear matter as well as in neutron-rich matter are reviewed.

Figures (12)

• Figure 1: Relative abundances of neutrons, $H$ and $He$ isotopes as a function of the excitation energy per nucleon of vaporized sources produced in collisions of $^{36}Ar$ and $^{58}Ni$ nuclei. Data are taken with the INDRA multidetector at GANIL. Curves represent fits using statistical (thermal) distributions of the different particle species after freeze-out. The corresponding (upper) temperature scale is also shown. (Adapted from Borderie et al., 2002).
• Figure 2: Caloric curve (temperature vs. excitation energy per nucleon) determined from different multifragmentation reactions as indicated. The temperature scale $T=T_{He\,Li}$ is derived from yield ratios of $He$ and $Li$ isotopes. Fit curves: $T=\sqrt{k\,E^*/A}$ with $k=10$ MeV corresponding to liquid phase (solid curve); $T={2\over 3}(E^*/A -\delta)$ with $\delta = 2$ MeV corresponding to gas phase (dashed curve). Figure adapted from Pochodzalla et al. (1995).
• Figure 3: Two isotherms of a Van der Waals type equation-of-state $P(n,T)$ in the vicinity of the critical point ($cp$). The starting and end points of the gas-liquid phase coexistence region for $T<T_c$ are marked by their densities $n_g$ and $n_l$, respectively. The horizontal dashed line illustrates the Maxwell construction.
• Figure 4: Two-pion exchange interaction between nucleons with an intermediate $\Delta N$ state involving the virtual excitation of a $\Delta(1230)$ baryonic resonance.
• Figure 5: Left panel: Schematic interaction potential (\ref{['eq:potential']}) that reproduces the empirical virial coefficient (\ref{['eq:Bcrit']}), $B(T_c)\simeq -17$ fm$^3$, at the critical temperature $T_c = 17.9$ MeV. The attractive part of the potential is based on two-pion exchange between nucleons with virtual excitation of the $\Delta(1230)$ baryonic resonance as sketched in Fig. \ref{['Fig4']} and indicated in the figure. Right panel: Plot of the integrand $F(r) = \exp(-{\cal V}(r)/T_c) - 1$ of the virial coefficient $B(T_c)$ (see eq. (\ref{['eq:integrand']})).