Analytical mass formula and nuclear surface properties in the ETF approximation

Abstract

The problem of the determination of the nuclear surface and surface symmetry energy is addressed in the framework of the Extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. For the case of symmetric nuclei, the resulting ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed, which cannot be simply deduced from the local part of the functional. In the case of asymmetric nuclei, 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 over previous models and leads to a precision better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

27 pages, 18 figures, submitted to PRC

References in corpus (12)

• Analytical representations of unified equations of state for neutron-star matter
• Symmetry Energy I: Semi-Infinite Matter
• Further improvements on a global nuclear mass model
• Inner crust of neutron stars with mass-fitted Skyrme functionals
• Neutron skin thickness in droplet model with surface width dependence: indications of softness of the nuclear symmetry energy
• Surface Symmetry Energy of Nuclear Energy Density Functionals
• Semi-classical equation of state and specific heats for neutron-star inner crust with proton shell corrections
• Light clusters, pasta phases and phase transitions in core-collapse supernova matter
• Densities and energies of nuclei in dilute matter
• New parameterization of Skyrme's interaction for regularized multi-reference energy density functional calculations
• Symmetry and Surface Symmetry Energies in Finite Nuclei
• In-medium nuclear cluster energies within the Extended Thomas-Fermi approach

Cited by in corpus (5)

• Nucleonic metamodelling in light of multimessenger, PREX-II and CREX data
• EoS constraints from nuclear masses and radii in a meta-modeling approach
• Properties of the neutron star crust: Quantifying and correlating uncertainties with improved nuclear physics
• Parametrization of the surface energy in the ETF approximation
• Towards an empirical unified crust-core description of neutron stars