dorsal/arxiv
View SchemaThomas-Fermi theory for atomic nuclei revisited
| Authors | M. Centelles, P. Schuck, X. Vinas |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0601092 |
| URL | https://arxiv.org/abs/nucl-th/0601092 |
| DOI | 10.1016/j.aop.2006.07.009 |
| Journal | Annals Phys.322:363-396,2007 |
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 hbar^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 hbar^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. 208Pb 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.
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"abstract": "The recently developed semiclassical variational Wigner-Kirkwood (VWK)\napproach is applied to finite nuclei using external potentials and\nself-consistent mean fields derived from Skyrme interactions and from\nrelativistic mean field theory. VWK consists of the Thomas-Fermi part plus a\npure, perturbative hbar^2 correction. In external potentials, VWK passes\nthrough the average of the quantal values of the accumulated level density and\ntotal energy as a function of the Fermi energy. However, there is a problem of\noverbinding when the energy per particle is displayed as a function of the\nparticle number. The situation is analyzed comparing spherical and deformed\nharmonic oscillator potentials. In the self-consistent case, we show for Skyrme\nforces that VWK binding energies are very close to those obtained from extended\nThomas-Fermi functionals of hbar^4 order, pointing to the rapid convergence of\nthe VWK theory. This satisfying result, however, does not cure the overbinding\nproblem, i.e., the semiclassical energies show more binding than they should.\nThis feature is more pronounced in the case of Skyrme forces than with the\nrelativistic mean field approach. However, even in the latter case the shell\ncorrection energy for e.g. 208Pb turns out to be only -6 MeV what is about a\nfactor two or three off the generally accepted value. As an ad hoc remedy,\nincreasing the kinetic energy by 2.5%, leads to shell correction energies well\nacceptable throughout the periodic table. The general importance of the present\nstudies for other finite Fermi systems, self-bound or in external potentials,\nis pointed out.",
"arxiv_id": "nucl-th/0601092",
"authors": [
"M. Centelles",
"P. Schuck",
"X. Vinas"
],
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"nucl-th"
],
"doi": "10.1016/j.aop.2006.07.009",
"journal_ref": "Annals Phys.322:363-396,2007",
"title": "Thomas-Fermi theory for atomic nuclei revisited",
"url": "https://arxiv.org/abs/nucl-th/0601092"
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