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Title: Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions

Abstract

We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic mean-field models. A model is developed that uses the generator coordinate method to perform configuration mixing calculations of angular-momentum-projected wave functions, calculated in a relativistic point-coupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the constrained relativistic mean-field + BCS equations in an axially deformed oscillator basis. A number of illustrative calculations are performed for the nuclei {sup 194}Hg and {sup 32}Mg, in comparison with results obtained in nonrelativistic models based on Skyrme and Gogny effective interactions.

Authors:
; ;  [1];  [2]
  1. Physics Department, Faculty of Science, University of Zagreb, Croatia, and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching (Germany)
  2. (Germany)
Publication Date:
OSTI Identifier:
20771331
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.73.034308; (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; ANGULAR MOMENTUM; APPROXIMATIONS; AXIAL SYMMETRY; COMPARATIVE EVALUATIONS; CONFIGURATION MIXING; COUPLING; FLUCTUATIONS; GENERATOR-COORDINATE METHOD; GEOMETRY; MAGNESIUM 32; MATHEMATICAL SOLUTIONS; MEAN-FIELD THEORY; MERCURY 194; NUCLEAR DEFORMATION; OSCILLATORS; QUADRUPOLES; RELATIVISTIC RANGE; SKYRME POTENTIAL; WAVE FUNCTIONS

Citation Formats

Niksic, T., Vretenar, D., Ring, P., and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions. United States: N. p., 2006. Web. doi:10.1103/PhysRevC.73.034308.
Niksic, T., Vretenar, D., Ring, P., & Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions. United States. doi:10.1103/PhysRevC.73.034308.
Niksic, T., Vretenar, D., Ring, P., and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Wed . "Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions". United States. doi:10.1103/PhysRevC.73.034308.
@article{osti_20771331,
title = {Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions},
author = {Niksic, T. and Vretenar, D. and Ring, P. and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching},
abstractNote = {We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic mean-field models. A model is developed that uses the generator coordinate method to perform configuration mixing calculations of angular-momentum-projected wave functions, calculated in a relativistic point-coupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the constrained relativistic mean-field + BCS equations in an axially deformed oscillator basis. A number of illustrative calculations are performed for the nuclei {sup 194}Hg and {sup 32}Mg, in comparison with results obtained in nonrelativistic models based on Skyrme and Gogny effective interactions.},
doi = {10.1103/PhysRevC.73.034308},
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 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
  • The framework of relativistic energy-density functionals 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-projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The effects of triaxial deformation and of K mixing is illustrated in a study of spectroscopic properties of low-spin states in {sup 24}Mg.
  • The recently developed structure model that uses the generator coordinate method to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes (3DAMP+GCM), is applied in a systematic study of ground states and low-energy collective states in the even-even magnesium isotopes {sup 20-40}Mg. Results obtained using a relativistic point-coupling nucleon-nucleon effective interaction in the particle-hole channel and a density-independent {delta} interaction in the pairing channel are compared to data and with previous axial 1DAMP+GCM calculations, both with a relativistic density functional and the nonrelativistic Gogny force. The effects of the inclusion ofmore » triaxial degrees of freedom on the low-energy spectra and E2 transitions of magnesium isotopes are examined.« less
  • We present a method based on mean-field states generated by triaxial quadrupole constraints that are projected on particle number and angular momentum and mixed by the generator coordinate method on the quadrupole moment. This method is equivalent to a seven-dimensional GCM calculation, mixing all five degrees of freedom of the quadrupole operator and the gauge angles for protons and neutrons. A first application to {sup 24}Mg permits a detailed analysis of the effects of triaxial deformations and of K mixing.