Thomas–Fermi theory for atomic nuclei revisited

Abstract

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative 2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of 4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g. 208 Pb turns out to be only ∼ −6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.

Relativistic Equation of State at Subnuclear Densities in the Thomas-Fermi Approximation

“…Many properties of nuclei can be described by the Thomas-Fermi approximation with good agreement to experimental data (Centelles et al 2007). Recently, the STF approximation has been used to study nuclear pasta phases at subnuclear densities at zero temperature (Avancini et al 2009) and finite temperature (Avancini et al 2010), where the pasta phases include droplets (bubbles), rods (tubes), and slabs for three, two, and one dimensions, respectively.…”

Effects of the symmetry energy on the isovector properties of neutron-rich nuclei within a Thomas-Fermi approach

“…The cut-off radius r c , which reflects the combined effect of the symmetry energy and Coulomb energy on the asymmetry function α(r) according to expression (19), easily can be determined by solving the equation…”

“…Actually there is a variety of neutron star properties which are sensitive to SE, that is the maximum mass value and the corresponding radius, the onset of the direct Urca process, the crust-core transition density and pressure e.t.c. [2,9] Recently, there is an extended theoretical [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,57,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,…”

Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy

“…In the past, mainly the Skyrme density functionals have been employed in the Extended Thomas Fermi theory [43][44][45][46]. They do not satisfy the identity (1).…”

“…We adopt an extended version of Thomas-Fermi (ETF) method which is based on the density functional approach [17,[43][44][45][46]. This technique has been extensively used in …”