skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Finite- to zero-range relativistic mean-field interactions

Abstract

We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the {sigma}-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

Authors:
; ; ;  [1];  [2];  [3]
  1. Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb (Croatia) and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching (Germany)
  2. (Greece)
  3. (Germany)
Publication Date:
OSTI Identifier:
21189820
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 77; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevC.77.034302; (c) 2008 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; BOSON-EXCHANGE MODELS; COLLECTIVE EXCITATIONS; COUPLING; GROUND STATES; INTERACTIONS; ISOVECTORS; MASS; MEAN-FIELD THEORY; MESON-NUCLEON INTERACTIONS; MESONS; NUCLEAR MATTER; NUCLEI; NUCLEONS; RELATIVISTIC RANGE; SCALARS

Citation Formats

Niksic, T., Vretenar, D., Lalazissis, G. A., Ring, P., Department of Theoretical Physics, Aristotle University of Thessaloniki, GR-54124, and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Finite- to zero-range relativistic mean-field interactions. United States: N. p., 2008. Web. doi:10.1103/PHYSREVC.77.034302.
Niksic, T., Vretenar, D., Lalazissis, G. A., Ring, P., Department of Theoretical Physics, Aristotle University of Thessaloniki, GR-54124, & Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Finite- to zero-range relativistic mean-field interactions. United States. doi:10.1103/PHYSREVC.77.034302.
Niksic, T., Vretenar, D., Lalazissis, G. A., Ring, P., Department of Theoretical Physics, Aristotle University of Thessaloniki, GR-54124, and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Sat . "Finite- to zero-range relativistic mean-field interactions". United States. doi:10.1103/PHYSREVC.77.034302.
@article{osti_21189820,
title = {Finite- to zero-range relativistic mean-field interactions},
author = {Niksic, T. and Vretenar, D. and Lalazissis, G. A. and Ring, P. and Department of Theoretical Physics, Aristotle University of Thessaloniki, GR-54124 and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching},
abstractNote = {We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the {sigma}-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.},
doi = {10.1103/PHYSREVC.77.034302},
journal = {Physical Review. C, Nuclear Physics},
number = 3,
volume = 77,
place = {United States},
year = {Sat Mar 15 00:00:00 EDT 2008},
month = {Sat Mar 15 00:00:00 EDT 2008}
}
  • We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit ofmore » the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.« less
  • Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions to the total energy that display an ultraviolet divergence are found. We propose a general strategy to regularize this divergence and we illustrate it in the case of the second-order corrections to the equation of state (EOS) of uniform symmetric matter. By setting a momentum cutoff {Lambda}, we show that for every (physically meaningful) value of {Lambda} it is possible to determine a new interaction such that the EOS withmore » the second-order corrections reproduces the empirical EOS, with a fit of the same quality as that obtained at the mean-field level.« less
  • The cross sections and analyzing powers for knockout from the 1{ital d}{sub 3/2}, 1{ital d}{sub 5/2}, and 2{ital s}{sub 1/2} states of {sup 40}Ca in the {sup 40}Ca({ital p},2{ital p}){sup 39}K reactions at {ital E}=200 and 300 MeV are analyzed with both zero-range and finite-range relativistic distorted-wave impulse approximation (DWIA) calculations. We employ the relativistic Love-Franey model for nucleon-nucleon {ital t} matrix and the global Dirac optical potentials by Hama {ital et} {ital al}. The finite-range calculations are performed by using the Monte Carlo method. The calculated analyzing powers at 300 MeV are in good agreement with the data exceptmore » the 1{ital d}{sub 5/2} state. The analyzing power in the finite-range calculation is more sensitive to the rms radius of the bound state wave function compared with the zero-range calculation. The extracted spectroscopic factors for {ital d} states in the finite-range calculation are closer to the values obtained by other reactions. The Monte Carlo method is effective to calculate the transition matrix elements included in the high partial waves of the distorted wave functions.« less
  • We study finite nuclei within the relativistic mean field approach with density dependent couplings (RMFD) based on the relativistic Brueckner-Hartree-Fock (RBHF) results on nuclear matter. We take the linear relativistic mean-field Lagrangian with mesons {sigma}, {omega}, {delta}, and {rho}, whose coupling constants with nucleons are determined so as to reproduce the RBHF results of nuclear matter at various densities and proton fractions. We apply the RMFD approach to various nuclei with spherical shape including unstable ones in the periodic table. We find satisfactory results on the nuclear properties. We emphasize here that the proton and neutron effective masses are largelymore » different from each other as the proton fraction is decreased from Y{sub p}=0.5, which forces us to include the isovector scalar meson {delta} in our approach. {copyright} {ital 1997} {ital The American Physical Society}« less
  • The equation of state for neutron matter at all temperatures is presented in a relativistic mean-field theory which describes known nuclear matter. Isotherms are calculated and discussed, and some limiting analytic forms of the equation of state are given. (NL)