Thermal properties of the nuclear surface

The thermal evolution of a few thermodynamic properties of the nuclear surface like its thermodynamic potential energy, entropy, and the symmetry free energy are examined for both semi-infinite nuclear matter and finite nuclei. The Thomas-Fermi model is employed. Three Skyrme interactions, namely, SkM${}^{*}$, SLy4, and SK255, are used for the calculations to gauge the dependence of the nuclear surface properties on the energy density functionals. For finite nuclei, the surface observables are computed from a global liquid-drop-inspired fit of the energies and free energies of a host of nuclei covering the entire periodic table. The hot nuclear system is modeled in a subtracted Thomas-Fermi framework. Compared to semi-infinite nuclear matter, substantial changes in the surface symmetry energy of finite nuclei are indicated; surface thermodynamic potential energies for the two systems are, however, not too different. Analytic expressions to fit the temperature and asymmetry dependence of the surface thermodynamic potential of semi-infinite nuclear matter and the temperature dependence of the surface free energy of finite nuclei are given.

Figure 1

The density profiles for liquid plus gas (${\rho }_{\lg }$) and gas (${\rho }_g$) for symmetric semi-infinite nuclear matter at $T$ = 10 MeV with the SLy4 interaction. The green-shaded region and the orange-shaded region represent the gas and the liquid density distributions, respectively.

Figure 2

Thermal evolution of the surface thermodynamic potential ${\sigma }_{\mu }$ of SINM with the SLy4, SkM${}^{*}$, and SK255 interactions. Panels (a)–(c) display results for $X=0.0$, 0.3, and 0.6, respectively.

Figure 3

The surface thermodynamic potential ${\sigma }_{\mu }$ of SINM with the three interactions plotted as a function of isospin asymmetry. Panels (a)–(c) show results at temperatures $T$ = 0.0, 5.0, and 10.0 MeV, respectively.

Figure 4

Thermal evolution of the surface symmetry free energy coefficient $f_s^{\mathrm{sym}}$ of SINM for the interactions SLy4, SkM${}^{*}$, and SK255.

Figure 5

The surface entropy per unit area of SINM shown as a function of temperature for the three interactions at asymmetries $X=0.0$, 0.3, and 0.6.

Figure 6

The surface entropy per unit area of SINM shown as a function of asymmetry for the three interactions at $T=4.0$ and 8.0 MeV.

Figure 7

Comparison of the thermal evolution of the surface free energy $f_s$ for finite nuclei (solid lines) and symmetric SINM (dashed lines) with the interactions SLy4, SkM${}^{*}$, and SK255.

Figure 8

Comparison of the thermal evolution of the surface symmetry free energy coefficients for finite nuclei (solid lines) and symmetric SINM (dashed lines) for the three interactions.