Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains

12 pags., 4 figs. -- PACS codes: 21.60.Jz, 21.65.Ef, 21.10.Gv, 21.30.FeThe 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 harmonicoscillator basis. In addition, two other density distributions of 208Pb, 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 by the HFBTHO code. 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.Three of the authors (M.K.G., A.N.A., and D.N.K) are grateful for support of the Bulgarian Science Fund under Contract No. DFNI-T02/19. D.N.K. thanks for the partial support from Contract No. DFNI-E02/6 of the Bulgarian Science Fund. E.M.G. and P.S. acknowledge support from MINECO (Spain) under Contract FIS2014–51971–P.Peer Reviewe