# Temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains

## TL;DR

This study examines how the symmetry energy and neutron skin thickness in Ni, Sn, and Pb isotopes change with temperature using Skyrme energy density functionals and various density models, revealing increased neutron skins at higher temperatures.

## Contribution

It introduces new methods to calculate the temperature-dependent symmetry energy coefficient within the local density approximation and compares different density distribution models.

## Key findings

- Symmetry energy decreases with temperature up to 4 MeV.
- Neutron radii and skins increase significantly with temperature.
- Effects are more pronounced in neutron-rich nuclei.

## Abstract

The temperature dependence of the symmetry energy for isotopic chains of even-even Ni, Sn, and Pb nuclei is investigated in the framework of the local density approximation (LDA). The Skyrme energy density functional with two Skyrme-class effective interactions, SkM* and SLy4, is used in the calculations. The temperature-dependent proton and neutron densities are calculated through the HFBTHO code that solves the nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical transformed deformed harmonic-oscillator basis. In addition, two other density distributions of $^{208}$Pb, namely the Fermi-type density determined within the extended Thomas-Fermi (TF) method and symmetrized-Fermi local density obtained within the rigorous density functional approach, are used. The kinetic energy densities are calculated either by the HFBTHO code or, for a comparison, by the extended TF method up to second order in temperature (with $T^{2}$ term). Alternative ways to calculate the symmetry energy coefficient within the LDA are proposed. The results for the thermal evolution of the symmetry energy coefficient in the interval $T=0-4$ MeV show that its values decrease with temperature. The temperature dependence of the neutron and proton root-mean-square radii and corresponding neutron skin thickness is also investigated, showing that the effect of temperature leads mainly to a substantial increase of the neutron radii and skins, especially in the more neutron-rich nuclei, a feature that may have consequences on astrophysical processes and neutron stars.