Abstract
We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas–Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.
Highlights
The determination of a reliable analytical or quasi-analytical mass formula, covering the whole nuclear mass table, is an important issue for applications of nuclear physics and nuclear astrophysics
It is interesting to analyze the δ dependence of the surface symmetry energy based on the fitted quadratic diffuseness: its sign is positive, which contrasts with studies based on liquid-drop parametrizations of the nuclear mass [5, 7, 29,30,31, 35]
In this paper we have addressed the problem of the determination of an analytical mass formula with coefficients directly linked to the different parameters of standard Skyrme functionals, in the extended Thomas–Fermi (ETF) approximation at second order in ÿ
Summary
The determination of a reliable analytical or quasi-analytical mass formula, covering the whole nuclear mass table, is an important issue for applications of nuclear physics and nuclear astrophysics. We present an extension of the work of Part I to the case of asymmetric nuclei, which requires the introduction of the proton and neutron density profiles as two independent degrees of freedom In this general case, the ETF energy integral cannot be evaluated analytically. Enough, this very crude approximation leads to an overestimation of HF energies of medium-heavy and heavy nuclei of no more than 200–400 keV/nucleon even for the most extreme dripline nuclei Such accuracy can be obtained only if both local and non-local terms in the energy functional are separately calculated, meaning that the symmetry energy does depend on bulk nuclear matter properties.
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