Temperature dependence of the volume and surface contributions to the nuclear symmetry energy within the coherent density fluctuation model

Abstract

The temperature dependence of the volume and surface components of the nuclear symmetry energy (NSE) and their ratio is investigated in the framework of the local density approximation (LDA). The results of these quantities for finite nuclei are obtained within the coherent density fluctuation model (CDFM). The CDFM weight function is obtained using the temperature-dependent proton and neutron densities calculated through the HFBTHO code that solves the nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical transformed deformed harmonic-oscillator basis. We present and discuss the values of the volume and surface contributions to the NSE and their ratio obtained for the Ni, Sn, and Pb isotopic chains around double-magic 78 Ni, 132 Sn, and 208 Pb nuclei. The results for the T -dependence of the considered quantities are compared with estimations made previously for zero temperature showing the behavior of the NSE components and their ratio, as well as with the available experimental data. The sensitivity of the results on various forms of the density dependence of the symmetry energy is studied. We confirm the existence of "kinks" of these quantities as functions of the mass number at T = 0 MeV for the double closed-shell nuclei 78 Ni and 132 Sn and the lack of "kinks" for the Pb isotopes, as well as the disappearance of these kinks as the temperature increases.

Symmetry energy properties of neutron-rich nuclei from the coherent density fluctuation model applied to nuclear matter calculations with Bonn potentials

“…5, the symmetry energy calculated with Bonn B potential is slightly smaller for ρ ≤ 0.25 fm −3 than the ones obtained from the Brueckner EDF and using the power parametrization [Eqs. (36) and (37)]. Nevertheless, the behavior of all symmetry energy curves is similar and in accordance with the empirical data [63][64][65] around the normal NM density.…”

“…Brueckner effective potential (from [16,17]) in a range of nuclear densities where the expression of symmetry energy derived from the effective Brueckner potential is non-negative. On the same figure we present for a comparison two other density dependencies S N M (ρ) used in our work [37]. These are the power parametrization (see Refs.…”

“…In our previous work [29] we have studied the temperature dependence of the nuclear symmetry energy S(A, T ), including its volume and surface [37] contributions as derived from Brueckner [31,38] and Skyrme [36] energy density functionals. In the present work we extract the symmetry energy coefficients in Ni, Sn, and Pb from many-body Brueckner-Hartree-Fock ground-state calculations of nuclear matter with realistic potentials (Bonn B and Bonn CD) at zero temperature (T = 0 MeV) by applying the CDFM using the finite nuclei densities obtained in self-consistent Hartree-Fock + BCS calculations with Skyrme effective interactions (SLy4, Sk3, and SGII).…”

“…Here we would like to comment on the following point. In the present work (and also in our previous paper [37]) we use Eq. (7) as a relation between the symmetry energy S(A) and its volume S V (A) and surface S S (A) components.…”

“…To avoid this constraint we adopt in our present work (and also in Ref. [37]) the relation from the droplet model [Eq. (7)].…”