Liquid-gas phase transition in infinite and finite nuclear systems

The liquid-gas phase transition in infinite asymmetric nuclear matter is studied with the ${\text{SkM}}^{*}$ interaction. In its light, the said transition is investigated in finite nuclei in a heated liquid-drop model where the drop is assumed to be in thermodynamic equilibrium with the vapor emanated from it. Results for caloric curve, isospin fractionation, heat capacity, and entropy are presented. The results of the calculations in this model are suggestive of a continuous phase transition.

Figure 1

The isotherms (full line) and the liquid-gas coexistence lines (dotted) for nuclear matter with asymmetry $X_0=0.193$ at temperatures 8.0, 11.0, and $14.1\text{MeV}$ are shown in the top panel; the middle panel shows the isotherms at $T=11.0\text{MeV}$ for different asymmetries as marked. The bottom panel displays the evolution of the average chemical potentials $⟨{\mu }_{sp}⟩$ for the single phase and $⟨{\mu }_{ce}⟩$ along the coexistence line.

Figure 2

Graphical representation of the phase equilibrium of infinite nuclear matter with $X_0=0.193$. For details, see the text.

Figure 3

The free energy per particle at 8 and $11\text{MeV}$ as a function of density. The full lines refer to the single phase; the dotted lines correspond to the mixed phase.

Figure 4

The isotherms and the coexistence lines for the nucleus ${}^{186}\mathrm{Re}$ at $T=6,8$, and $10\text{MeV}$ (top panel); the bottom panel shows the average chemical potential as a function of density. The symbols have the same meaning as in Fig. 1.

Figure 5

Isotherms and the coexistence lines for the systems ${}^{186}\mathrm{Re},{}^{150}\mathrm{Re}$, and ${}^{50}\mathrm{Ca}$ at $T=8\text{MeV}$.

Figure 6

The particle fraction (top panel), the proton fraction (middle panel), and the density (bottom panel) of the liquid (left) and the gas (right) phases with Coulomb interaction switched off at $T=8\text{MeV}$ for nuclear matter $\left(X_0=0.193\right)$, ${}^{186}\mathrm{Re}$ and ${}^{50}\mathrm{Ca}$.

Figure 7

Same as Fig. 6, but with Coulomb interaction on.

Figure 8

Evolution of proton fraction along the liquid-gas coexistence line at $T=8\text{MeV}$ for the systems as shown.

Figure 9

The liquid particle fraction (a), the proton fraction in the liquid and gas phase (b), the liquid (c) and the gas (d) densities on the coexistence lines as a function of temperature at “freeze-out” volumes five and ten times the normal nuclear volume $V_0$ for the system ${}^{186}\mathrm{Re}$.

Figure 10

Caloric curves at constant pressures (as shown) for nuclear matter $\left(X_0=0.193\right)$ and ${}^{186}\mathrm{Re}$.

Figure 11

Heat capacity at constant pressure (as shown) for nuclear matter $\left(X_0=0.193\right)$ and ${}^{186}\mathrm{Re}$.

Figure 12

Thermal evolution of entropy per particle at constant pressure for nuclear matter $\left(X_0=0.193\right)$ and ${}^{186}\mathrm{Re}$.