Refined Thomas-Fermi description of hot nuclei

Abstract

Self-consistent density profiles of two-component hot nuclei in equilibrium with an external gas are calculated in the semi-classical Thomas-Fermi model with a new prescription. The energy functional is calculated with a momentum and density dependent finite range two-body effective interaction. The evolution of equilibrium nuclear masses as a function of temperature and densities of the external neutron and proton gas is investigated in this description. Limiting temperatures of nuclei, their lifetimes against neutron evaporation, temperature dependence of incompressibilites of finite nuclei and a few other observables are also studied in the present model.

Temperature dependence of the symmetry energy of finite nuclei

“…The Seyler-Blanchard [19] interaction has also been very successfully used by Myers and Swiatecki [20,21] in the context of the nuclear mass formula. The modified version of this interaction (SBM) is found to reproduce the ground state binding energies, charge rms radii, Giant Monopole Resonance (GMR) energies etc., very well for a host of nuclei from 16 O to very heavy systems [14,22]. The properties of pure neutron matter calculated with this type of interaction is also seen to be in good agreement [23] with those obtained from other sophisticated interactions.…”

“…These parameters differ somewhat from the ones used in Ref. [14] where the volume symmetry coefficient e sym was taken as 34 MeV. In the present communication, it is taken as 31 MeV, a value commonly used by several authors with some justification from experimental findings [3].…”

“…The details for obtaining the density in this method for the SkM * force are given in Ref. [15]; for the SBM interaction, they have also been presented earlier [14,24]. However, for completeness, we present the salient features below.…”

“…Finite temperature ThomasFermi framework with the subtraction technique [12] has been employed for this purpose. Two effective interactions, namely the modified Seyler-Blanchard (SBM) [13,14] and the SkM * [15] interactions that give practically the same symmetry coefficient (∼ 31 MeV) at their respective saturation densities have been used in our calculations. Dynamical changes in the energy mass m ω with temperature is also taken into account following the prescription of Refs.…”

Small damping approach in Fermi-liquid theory

“…We have here adopted the value of α = 9.2 MeV from [5], which corresponds to σ in ≈ σ free /2, where σ free ≈ 40 mb is the cross section for the nucleon-nucleon scattering in free space. Theoretical speculations and possible experimental indications of a limiting temperature suggest T lim ≈ 5 − 7 MeV [30][31][32]. Thus, here and below we have plotted the figures for temperatures up to 7 MeV.…”