From finite nuclei to the nuclear liquid drop: Leptodermous expansion based on self-consistent mean-field theory

P.-G. Reinhard, M. Bender, W. Nazarewicz, and T. Vertse
Phys. Rev. C 73, 014309 – Published 24 January 2006

Abstract

The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the nonrelativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A1/3 (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 106. The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.

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  • Received 11 October 2005

DOI:https://doi.org/10.1103/PhysRevC.73.014309

©2006 American Physical Society

Authors & Affiliations

P.-G. Reinhard1,2, M. Bender3,4,5, W. Nazarewicz6,7,8, and T. Vertse2,9,10

  • 1Institut für Theoretische Physik II, Universität Erlangen-Nürnberg, Staudtstrasse 7, D-91058 Erlangen, Germany
  • 2Joint Institute for Heavy Ion Research, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831, USA
  • 3Institute for Nuclear Theory, University of Washington, Box 351550, Seattle, Washington 98195-1550, USA
  • 4Physics Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439, USA
  • 5National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA
  • 6Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
  • 7Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831, USA
  • 8Institute of Theoretical Physics, Warsaw University, ul. Hoża 69, PL-00681, Warsaw, Poland
  • 9Institute of Nuclear Research of the Hungarian Academy of Sciences (Atomki) P.O. Box 51, H-4001, Debrecen, Hungary
  • 10University of Debrecen, Faculty of Informatics, H-4001, Debrecen, P.O. Box 12, Hungary

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Vol. 73, Iss. 1 — January 2006

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