Analysis of semiclassical approximations in the framework of quantumhadrodynamics

Speicher, Christoph; Engel, E.; Dreizler, R. M.

doi:10.1016/0375-9474(93)90130-p

Cited by 27 publications

(29 citation statements)

References 36 publications

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“…The semiclassical relativistic extended Thomas-Fermi (RETF) approach [55][56][57][58][59] has recently been applied in scaling and constrained calculations of the GMR energy in stable isotopes in [60,61]. The results turn out to be in good agreement with the values extracted from full relativistic RPA calculations [60,61].…”

Section: Introductionsupporting

confidence: 74%

“…As in the nonrelativistic problem, the theory can be formulated in the ThomasFermi approach. When corrections of order 2 (in gradients of the nucleon densities and of the Dirac effective mass) to the pure Thomas-Fermi contribution are included in the energy density, it is known as the relativistic extended Thomas-Fermi approach [55][56][57][58][59].…”

Section: Formalismmentioning

confidence: 99%

“…Following [55][56][57][58], in the relativistic extended Thomas-Fermi approach the expression of the nucleonic part E is written as E = E 0 + E 2 , where 1/2 of the effective particle, with q = n for neutrons and q = p for protons. The coefficients C iq stand for the following analytic functions of k Fq and m * = m − Φ: …”

Section: Appendix A: Equations Of the Relativistic Extended Thomas-fementioning

confidence: 99%

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The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas–Fermi theory

Centelles¹,

Patra²,

Roca-Maza³

et al. 2010

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

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We analyze the influence of the density dependence of the symmetry energy on the average excitation energy of the isoscalar giant monopole resonance (GMR) in stable and exotic neutron-rich nuclei by applying the relativistic extended Thomas-Fermi method in scaling and constrained calculations. For the effective nuclear interaction, we employ the relativistic mean field model supplemented by an isoscalar-isovector meson coupling that allows one to modify the density dependence of the symmetry energy without compromising the success of the model for binding energies and charge radii. The semiclassical estimates of the average energy of the GMR are known to be in good agreement with the results obtained in full RPA calculations. The present analysis is performed along the Pb and Zr isotopic chains. In the scaling calculations, the excitation energy is larger when the symmetry energy is softer. The same happens in the constrained calculations for nuclei with small and moderate neutron excess. However, for nuclei of large isospin the constrained excitation energy becomes smaller in models having a soft symmetry energy. This effect is mainly due to the presence of loosely-bound outer neutrons in these isotopes. A sharp increase of the estimated width of the resonance is found in largely neutron-rich isotopes, even for heavy nuclei, which is enhanced when the symmetry energy of the model is soft. The results indicate that at large neutron numbers the structure of the low-energy region of the GMR strength distribution changes considerably with the density dependence of the nuclear symmetry energy, which may be worthy of further characterization in RPA calculations of the response function.

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Section: Introductionsupporting

confidence: 74%

Section: Formalismmentioning

confidence: 99%

Section: Appendix A: Equations Of the Relativistic Extended Thomas-fementioning

confidence: 99%

See 1 more Smart Citation

The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas–Fermi theory

Centelles¹,

Patra²,

Roca-Maza³

et al. 2010

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

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“…The properties of SINM have gained a lot of attention as well, see e.g. [21,23,39,[42][43][44][45][46] for non-relativistic models and [47][48][49][50][51][52][53][54] for relativistic interactions. We just want to repeat the findings relevant for our study, Table 1 summarises the coefficients of (10) as calculated from symmetric INM and SINM for a number of effective interactions.…”

Section: Nuclear Matter Propertiesmentioning

confidence: 99%

Consequences of the center–of–mass correction in nuclear mean–field models

Bender

Rutz

Reinhard

et al. 2000

EPJ A

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Abstract.We study the influence of the scheme for the correction for spurious center-of-mass motion on the fit of effective interactions for self-consistent nuclear mean-field calculations. We find that interactions with very simple center-of-mass correction have significantly larger surface coefficients than interactions for which the center-of-mass correction was calculated for the actual many-body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center-of-mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei.

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“…QHDII, and applications to finite, thermal nuclear systems will be given in a forthcoming publication. The present work is a sequel to the global density functional approach to QHD at T= 0 given in a previous publication [7]. We rely on this work for details concerning questions of renormalization, which are independent of temperature, and, to a good measure, on the notation used there.…”

Section: Introductionmentioning

confidence: 99%

Extended density functional approach to nuclear systems at finite temperature

Müller

Dreizler

1992

Z. Physik A - Hadrons and Nuclei

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We present a density functional description of Quantumhadrodynamics at finite temperature. As a basic foundation we generalize Mermin's existence theorem for thermal systems to the case of a thermal field theory. An explicit functional for the free energy involving gradient corrections to second order and meson exchange in the Hartree approximation is constructed. This density functional model can be shown to be an approximation of Waleckas mean field approach for finite nuclear systems at T#:0. PACS: 21.65. +f; 05.30.Fk

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Analysis of semiclassical approximations in the framework of quantumhadrodynamics

Cited by 27 publications

References 36 publications

The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas–Fermi theory

The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas–Fermi theory

Consequences of the center–of–mass correction in nuclear mean–field models

Extended density functional approach to nuclear systems at finite temperature

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