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Title: Thomas-Fermi theory of the breathing mode and nuclear incompressibility

Abstract

A Thomas-Fermi theory with a linear scaling assumption is proposed for the breathing mode of nuclear collective motion. It leads to a general result K{sub A}={l_angle}K({rho},{delta}){r_angle}+K{sub GD}{minus}2E{sub C}/A which states that the incompressibility K{sub A} of a finite nucleus A mainly equals the nuclear matter incompressibility K({rho},{delta}) averaged over the nucleon density distribution {rho}({bold r}) of nucleus A, added to a term K{sub GD} contributed from the gradients of nucleon densities, with twice the Coulomb energy per nucleon E{sub C}/A subtracted. The nuclear matter equation of state given by the Thomas-Fermi statistical model with a Seyler-Blanchard-type interaction is employed to calculate the nuclear matter incompressibility K({rho},{delta}) and a localized approximation of the Seyler-Blanchard-type interaction, which is shown to be similar to the Skyrme-type interaction, is developed to calculate the value of K{sub GD}. K{sub GD} and {minus}2E{sub C}/A contribute about 20{endash}10{percent} and 1{endash}5{percent}, respectively, to the nuclear incompressibility K{sub A}, from the light to the heavy nuclei. The shell and the even-odd effects are discussed by a scaling model which shows that these effects can be neglected for medium and heavy nuclei. The anharmonic effect is shown to be significant only for light nuclei. The leptodermous expansion of K{sub A}more » is obtained and the contribution from the curvature term proportional to A{sup {minus}2/3} is discussed. The calculated isoscalar giant monopole resonance energy E{sub M} for a variety of nuclei are shown to be in agreement with experimental measurements. {copyright} {ital 1997} {ital The American Physical Society}« less

Authors:
; ;  [1]
  1. Departamento de Fisica Nuclear e Altas Energias, Instituto de Fisica, Universidade do Estado do Rio de Janeiro, Rio de Janeiro-RJ 20559-900 (Brazil)
Publication Date:
OSTI Identifier:
509091
Resource Type:
Journal Article
Journal Name:
Physical Review, C
Additional Journal Information:
Journal Volume: 55; Journal Issue: 6; Other Information: PBD: Jun 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; THOMAS-FERMI MODEL; COLLECTIVE MODEL; NUCLEAR MATTER; COMPRESSIBILITY; NUCLEAR FORCES; SCALING; DENSITY; NUCLEONS; HEAVY NUCLEI; GIANT RESONANCE; MONOPOLES; BREATH

Citation Formats

Wang, C S, Chung, K C, and Santiago, A J. Thomas-Fermi theory of the breathing mode and nuclear incompressibility. United States: N. p., 1997. Web. doi:10.1103/PhysRevC.55.2844.
Wang, C S, Chung, K C, & Santiago, A J. Thomas-Fermi theory of the breathing mode and nuclear incompressibility. United States. https://doi.org/10.1103/PhysRevC.55.2844
Wang, C S, Chung, K C, and Santiago, A J. Sun . "Thomas-Fermi theory of the breathing mode and nuclear incompressibility". United States. https://doi.org/10.1103/PhysRevC.55.2844.
@article{osti_509091,
title = {Thomas-Fermi theory of the breathing mode and nuclear incompressibility},
author = {Wang, C S and Chung, K C and Santiago, A J},
abstractNote = {A Thomas-Fermi theory with a linear scaling assumption is proposed for the breathing mode of nuclear collective motion. It leads to a general result K{sub A}={l_angle}K({rho},{delta}){r_angle}+K{sub GD}{minus}2E{sub C}/A which states that the incompressibility K{sub A} of a finite nucleus A mainly equals the nuclear matter incompressibility K({rho},{delta}) averaged over the nucleon density distribution {rho}({bold r}) of nucleus A, added to a term K{sub GD} contributed from the gradients of nucleon densities, with twice the Coulomb energy per nucleon E{sub C}/A subtracted. The nuclear matter equation of state given by the Thomas-Fermi statistical model with a Seyler-Blanchard-type interaction is employed to calculate the nuclear matter incompressibility K({rho},{delta}) and a localized approximation of the Seyler-Blanchard-type interaction, which is shown to be similar to the Skyrme-type interaction, is developed to calculate the value of K{sub GD}. K{sub GD} and {minus}2E{sub C}/A contribute about 20{endash}10{percent} and 1{endash}5{percent}, respectively, to the nuclear incompressibility K{sub A}, from the light to the heavy nuclei. The shell and the even-odd effects are discussed by a scaling model which shows that these effects can be neglected for medium and heavy nuclei. The anharmonic effect is shown to be significant only for light nuclei. The leptodermous expansion of K{sub A} is obtained and the contribution from the curvature term proportional to A{sup {minus}2/3} is discussed. The calculated isoscalar giant monopole resonance energy E{sub M} for a variety of nuclei are shown to be in agreement with experimental measurements. {copyright} {ital 1997} {ital The American Physical Society}},
doi = {10.1103/PhysRevC.55.2844},
url = {https://www.osti.gov/biblio/509091}, journal = {Physical Review, C},
number = 6,
volume = 55,
place = {United States},
year = {1997},
month = {6}
}