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Title: Charge and parity projected relativistic mean field model with pion for finite nuclei

Abstract

We construct a new relativistic mean field model by explicitly introducing a {pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral {sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the {sup 4}He nucleus as a pilot case and study the role of the {pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of {sup 4}He by varying several parameters, such as the {sigma}-meson mass and the {omega}-meson coupling constant. We are able to construct a good ground state for {sup 4}He. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of {sup 4}He are naturally obtained in the CPPRMF model.

Authors:
; ; ; ;  [1];  [2];  [3]
  1. Research Center for Nuclear Physics (RCNP), Osaka University, Osaka 567-0047 (Japan)
  2. (Japan)
  3. (RIKEN), Wako, Saitama 351-0198 (Japan)
Publication Date:
OSTI Identifier:
20771324
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevC.73.034301; (c) 2006 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; ALPHA PARTICLES; ATOMIC NUMBER; CHIRAL SYMMETRY; CORRELATIONS; COUPLING CONSTANTS; FORM FACTORS; GROUND STATES; HELIUM 4; LAGRANGIAN FUNCTION; MEAN-FIELD THEORY; NONLINEAR PROBLEMS; NUCLEAR MATTER; NUCLEAR MODELS; OMEGA-782 MESONS; PARITY; PIONS; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; SIGMA MODEL

Citation Formats

Ogawa, Yoko, Toki, Hiroshi, Tamenaga, Setsuo, Sugimoto, Satoru, Ikeda, Kiyomi, Department of Physics, Kyoto University, Kyoto 606-8502, and Institute of Physical and Chemical Research. Charge and parity projected relativistic mean field model with pion for finite nuclei. United States: N. p., 2006. Web. doi:10.1103/PhysRevC.73.034301.
Ogawa, Yoko, Toki, Hiroshi, Tamenaga, Setsuo, Sugimoto, Satoru, Ikeda, Kiyomi, Department of Physics, Kyoto University, Kyoto 606-8502, & Institute of Physical and Chemical Research. Charge and parity projected relativistic mean field model with pion for finite nuclei. United States. doi:10.1103/PhysRevC.73.034301.
Ogawa, Yoko, Toki, Hiroshi, Tamenaga, Setsuo, Sugimoto, Satoru, Ikeda, Kiyomi, Department of Physics, Kyoto University, Kyoto 606-8502, and Institute of Physical and Chemical Research. Wed . "Charge and parity projected relativistic mean field model with pion for finite nuclei". United States. doi:10.1103/PhysRevC.73.034301.
@article{osti_20771324,
title = {Charge and parity projected relativistic mean field model with pion for finite nuclei},
author = {Ogawa, Yoko and Toki, Hiroshi and Tamenaga, Setsuo and Sugimoto, Satoru and Ikeda, Kiyomi and Department of Physics, Kyoto University, Kyoto 606-8502 and Institute of Physical and Chemical Research},
abstractNote = {We construct a new relativistic mean field model by explicitly introducing a {pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral {sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the {sup 4}He nucleus as a pilot case and study the role of the {pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of {sup 4}He by varying several parameters, such as the {sigma}-meson mass and the {omega}-meson coupling constant. We are able to construct a good ground state for {sup 4}He. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of {sup 4}He are naturally obtained in the CPPRMF model.},
doi = {10.1103/PhysRevC.73.034301},
journal = {Physical Review. C, Nuclear Physics},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • The pion plays an important role in a nucleus. Until now, its effect was treated in terms of the Brueckner theory in nuclear matter through the G-matrix effective interaction. The difficulty of handling the pion exchange interaction in a finite nucleus is through the strong tensor interaction due to the pion exchange. The tensor optimized shell model (TOSM) together with the unitary correlation operator method (UCOM) was demonstrated to provide a quantitative account of tensor correlation in a finite nucleus. We discuss in this paper the recently developed relativistic chiral mean field model for finite nuclei by taking the conceptmore » of TOSM and UCOM.« less
  • We introduce first the facilities of RCNP; the cyclotron facility and GeV gamma facility. We discuss then the role of the pion on the ground state of finite nuclei. We treat the pions in the relativistic mean field approximation with the projection of the parity and the charge number by using the chiral Lagrangian, We find good ground state properties of 4He.
  • The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent {delta}-interaction in the pairing channel. Illustrative calculations aremore » performed for {sup 24}Mg, {sup 32}S, and {sup 36}Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions.« 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
  • In the relativistic quantum mean field theory retardation effects are investigated for spherical nuclei throughout the Periodic Table. In a Hartree-Fock calculation retardation affects only the exchange terms; the exchange of {sigma}, {omega}, {rho}, and {pi} mesons and photons are included. We find the retardation is important only for the pion; for the other heavier mesons its contribution is negligibly small. The total binding energy of a nucleus can be changed by about 5% when retardation is included. For the electric charge density appreciable difference is observed only for {sup 208}Pb.