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Title: Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei

Abstract

Correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock model. From the most recent analysis of the isospin diffusion data in heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections, a value of L=88{+-}25 MeV for the slope of the nuclear symmetry energy at saturation density is extracted, and this imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Predicted thickness of the neutron skin is 0.22{+-}0.04 fm for {sup 208}Pb, 0.29{+-}0.04 fm for {sup 132}Sn, and 0.22{+-}0.04 fm for {sup 124}Sn.

Authors:
 [1];  [2];  [3];  [4]
  1. Institute of Theoretical Physics, Shanghai Jiao Tong University, Shanghai 200240 (China)
  2. (China)
  3. Cyclotron Institute and Physics Department, Texas A and M University, College Station, Texas 77843-3366 (United States)
  4. Department of Chemistry and Physics, P.O. Box 419, Arkansas State University, State University, Arkansas 72467-0419 (United States)
Publication Date:
OSTI Identifier:
20771086
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevC.72.064309; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CORRELATIONS; CROSS SECTIONS; DIFFUSION; HARTREE-FOCK METHOD; HEAVY ION REACTIONS; ISOSPIN; LEAD 208; MEV RANGE; NEUTRONS; NUCLEAR MATTER; SKIN; SKYRME POTENTIAL; SYMMETRY; THICKNESS; TIN 124; TIN 132; TRANSPORT THEORY

Citation Formats

Chen Liewen, Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, Ko, C.M., and Li Baoan. Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei. United States: N. p., 2005. Web. doi:10.1103/PhysRevC.72.064309.
Chen Liewen, Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, Ko, C.M., & Li Baoan. Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei. United States. doi:10.1103/PhysRevC.72.064309.
Chen Liewen, Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, Ko, C.M., and Li Baoan. Thu . "Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei". United States. doi:10.1103/PhysRevC.72.064309.
@article{osti_20771086,
title = {Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei},
author = {Chen Liewen and Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000 and Ko, C.M. and Li Baoan},
abstractNote = {Correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock model. From the most recent analysis of the isospin diffusion data in heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections, a value of L=88{+-}25 MeV for the slope of the nuclear symmetry energy at saturation density is extracted, and this imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Predicted thickness of the neutron skin is 0.22{+-}0.04 fm for {sup 208}Pb, 0.29{+-}0.04 fm for {sup 132}Sn, and 0.22{+-}0.04 fm for {sup 124}Sn.},
doi = {10.1103/PhysRevC.72.064309},
journal = {Physical Review. C, Nuclear Physics},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness {Delta}r{sub np} of Sn isotopes give an important constraint on the symmetry energy E{sub sym}({rho}{sub 0}) and its density slope L at saturation density {rho}{sub 0}. Combining these constraints with those from recent analyses of isospin diffusion and the double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringentmore » limit on L approximately independent of E{sub sym}({rho}{sub 0}). The implication of these new constraints on the {Delta}r{sub np} of {sup 208}Pb as well as the core-crust transition density and pressure in neutron stars is discussed.« less
  • We describe a relation between the symmetry energy coefficients c{sub sym}({rho}) of nuclear matter and a{sub sym}(A) of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of c{sub sym}({rho}). Here, we take advantage of this relation to explore the prospects for constraining c{sub sym}({rho}) of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.
  • The density dependence of the symmetry energy, characterized by the parameter L, is studied using information provided by the neutron skin thickness in finite nuclei. An estimate of L is obtained from experimental data of antiprotonic atoms. We also discuss the ability of parity violating electron scatering to obtain information about the neutron skin thickness in {sup 208}Pb.
  • We analyze the neutron skin thickness in finite nuclei with the droplet model and effective nuclear interactions. The ratio of the bulk symmetry energy J to the so-called surface stiffness coefficient Q has in the droplet model a prominent role in driving the size of neutron skins. We present a correlation between the density derivative of the nuclear symmetry energy at saturation and the J/Q ratio. We emphasize the role of the surface widths of the neutron and proton density profiles in the calculation of the neutron skin thickness when one uses realistic mean-field effective interactions. Next, taking as experimentalmore » baseline the neutron skin sizes measured in 26 antiprotonic atoms along the mass table, we explore constraints arising from neutron skins on the value of the J/Q ratio. The results favor a relatively soft symmetry energy at subsaturation densities. Our predictions are compared with the recent constraints derived from other experimental observables. Though the various extractions predict different ranges of values, one finds a narrow window L{approx}45-75 MeV for the coefficient L that characterizes the density derivative of the symmetry energy that is compatible with all the different empirical indications.« less
  • Correlations among several nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We show analytically a singularity at the incompressibility K{sub c}=306 MeV in correlations between the isovector nuclear matter properties and incompressibility with the SHF model, whereas there is no obvious singularity in those correlations with the RMF model. A linearmore » correlation between the neutron skin thickness and the pressure of the neutron matter is given in terms of the ratio between the neutron and nuclear matter densities in the SHF model. We show that the neutron skin thickness gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of the Skyrme interaction.« less