Variational Wigner–Kirkwood ℏ Expansion

Centelles, M.; Viñas, X.; Durand, M.; Schuck, Peter; Von-Eiff, D.

doi:10.1006/aphy.1998.5792

Cited by 21 publications

(65 citation statements)

References 39 publications

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“…It is found that as in the case of the quantal density matrix, the Extended Thomas-Fermi approximation sums all the momentum weighted integrals [8], Although the Extended Thomas-Fermi approach applied to a non-local one-body Hamiltonian gives reasonably good results, to improve this semiclassical approximation by adding the fullh 4 -order contributions seems to be in order. Another way of improving the semiclassical results presented here to obtain the smooth part of the energy is by using the Variational WignerKirkwood approach [15] which slightly differs from the Extended Thomas-Fermi approximation presented in this paper. We reserve these extensions of the semiclassical calculations in the non-local case for a future work.…”

Section: Discussionmentioning

confidence: 99%

“…The semiclassical distribution function f (R, p) is a representation of the true phase-space function in terms of distributions and is very efficient in order to obtain semiclassical expectation values by integrals over the whole phase-space [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…The main purpose of this paper is to derive the explicit expression of the DM in the Extended Thomas-Fermi (ETF) approximation [16] starting from the very recently presented WK expansion up toh 2 order of the distribution function for non-local potentials [15]. On one hand, we want to establish a link between the NV (and CB) expansions of the DM with this semiclassical approach and, on the other, to apply this ETF DM to derive the exchange HF energy when finite range forces are used.…”

Section: Introductionmentioning

confidence: 99%

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Extended Thomas–Fermi approximation to the one-body density matrix

Soubbotin

Viñas

2000

Nuclear Physics A

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The one-body density matrix is derived within the Extended Thomas-Fermi approximation. This has been done starting from the Wigner-Kirkwood distribution function for a non-local single-particle potential. The links between this new approach to the density matrix with former ones available in the literature are widely discussed. The semiclassical Hartree-Fock energy at Extended Thomas-Fermi level is also obtained in the case of a non-local one-body Hamiltonian. Numerical applications are performed using the Gogny and Brink-Boeker effective interactions. The semiclassical binding energies and root mean square radii are compared with the fully quantal ones and with those obtained using the Strutinsky averaged method.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended Thomas–Fermi approximation to the one-body density matrix

Soubbotin

Viñas

2000

Nuclear Physics A

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“…The method for solving this variational problem [11,12], which sorts out properly the different powers of at each step of the minimization, was called variational WignerKirkwood (VWK) theory. This VWK method has been applied to describe half infinite nuclear matter in the self consistent case using Skyrme forces [12] and the relativistic mean field approximation [13]. The formal VWK approach, up to 4 order, was developed in [12].…”

Section: Introductionmentioning

confidence: 99%

“…This VWK method has been applied to describe half infinite nuclear matter in the self consistent case using Skyrme forces [12] and the relativistic mean field approximation [13]. The formal VWK approach, up to 4 order, was developed in [12]. Another related approach widely used for dealing with the semiclassical approximation of the self consistent HF problem, is based on the so-called density functional theory (DFT).…”

Section: Introductionmentioning

confidence: 99%

Thomas–Fermi theory for atomic nuclei revisited

2007

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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.

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One-particle exchange in the double-folded potential in a semiclassical approximation

Soubbotin

Viñas

1999

J. Phys. G: Nucl. Part. Phys.

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The one-particle exchange in the double folded model is analyzed. To this aim the Extended Thomas-Fermi approach to the one-body density matrix is used. The nucleonnucleon force with Yukawa, Gauss and Coulomb-type form factors are considered. The energy dependence of the exchange part of the double folded potential is investigated and a comparison of the present approach with former ones is carried out.

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Variational Wigner–Kirkwood ℏ Expansion

Cited by 21 publications

References 39 publications

Extended Thomas–Fermi approximation to the one-body density matrix

Extended Thomas–Fermi approximation to the one-body density matrix

Thomas–Fermi theory for atomic nuclei revisited

One-particle exchange in the double-folded potential in a semiclassical approximation

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