Thomas-Fermi theory for atomic nuclei revisited

Journal Article · Thu Feb 15 04:00:00 EST 2007 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2006.07.009· OSTI ID:20976729

Centelles, M ^[1]; Schuck, P ^[2]; Vinas, X ^[1]

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1. Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona (Spain)
2. Institut de Physique Nucleaire, IN2P3-CNRS, Universite Paris-Sud, 91406 Orsay-Cedex (France)

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 h {sup 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 h {sup 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., {sup 208}Pb turns out to be only {approx}-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.

• OSTI ID: 20976729
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 322; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BINDING ENERGY
CONVERGENCE
CORRECTIONS
ENERGY-LEVEL DENSITY
FUNCTIONALS
HARMONIC OSCILLATORS
KINETIC ENERGY
LEAD 208
MEAN-FIELD THEORY
MEV RANGE 01-10
RELATIVISTIC RANGE
SEMICLASSICAL APPROXIMATION
SKYRME POTENTIAL
SPHERICAL CONFIGURATION
THOMAS-FERMI MODEL
VARIATIONAL METHODS