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Title: Particle-number projection in the finite-temperature mean-field approximation

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1368622
Grant/Contract Number:
FG02-91ER40608; FG02-00ER411132
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 96; Journal Issue: 1; Related Information: CHORUS Timestamp: 2017-07-07 22:09:33; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Fanto, P., Alhassid, Y., and Bertsch, G. F. Particle-number projection in the finite-temperature mean-field approximation. United States: N. p., 2017. Web. doi:10.1103/PhysRevC.96.014305.
Fanto, P., Alhassid, Y., & Bertsch, G. F. Particle-number projection in the finite-temperature mean-field approximation. United States. doi:10.1103/PhysRevC.96.014305.
Fanto, P., Alhassid, Y., and Bertsch, G. F. 2017. "Particle-number projection in the finite-temperature mean-field approximation". United States. doi:10.1103/PhysRevC.96.014305.
@article{osti_1368622,
title = {Particle-number projection in the finite-temperature mean-field approximation},
author = {Fanto, P. and Alhassid, Y. and Bertsch, G. F.},
abstractNote = {},
doi = {10.1103/PhysRevC.96.014305},
journal = {Physical Review C},
number = 1,
volume = 96,
place = {United States},
year = 2017,
month = 7
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 7, 2018
Publisher's Accepted Manuscript

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  • 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 effects of current quark masses on chiral-symmetry breaking in QCD at finite temperature are examined using a mean-field approximation. The current quark mass plays a role analogous to that of an external magnetic field in the ferromagnetic transition, as it explicitly violates the chiral symmetry whose restoration characterizes the phase transition. For small enough masses, the order parameter, related to the quark condensate, maintains the features of the massless case up to the critical temperature, and then it approaches a constant value depending on the current mass term itself. The consequences on the behavior of the pion mass andmore » decay constant are also studied. Our calculations are done with a variational composite operator approach. We also discuss the critical exponents (in temperature, mass, and for susceptibility) that follow in general from assuming the possible validity of a Landau mean-field theory.« 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.
  • We calculate the finite nucleus Dirac mean field spectrum in a Galerkinapproach using finite basis splines. We review the method and present resultsfor the relativistic sigma-..omega.. model for the closed-shell nuclei/sup 16/O and /sup 40/Ca. We study the convergence of themethod as a function of the size of the basis and the closure properties of thespectrum using an energy-weighted dipole sum rule. We apply the method to theDirac random-phase-approximation response and present results for the isoscalar1/sup /minus// and 3/sup /minus// longitudinal form factors of/sup 16/O and /sup 40/Ca. We also use a /ital B/-splinespectral representation of the positive-energy projector tomore » evaluate partialenergy-weighted sum rules and compare with nonrelativistic sum rule results.« less
  • The Lipkin-Nogami method is generalized to deal with finite range density dependent forces. New expressions are derived and realistic calculations with the Gogny force are performed for the nuclei {sup 164}Er and {sup 168}Er. The sharp phase transition predicted by the mean field approximation is washed out by the Lipkin-Nogami approach. A much better agreement with the experimental data is reached with the new approach than with the Hartree-Fock-Bogoliubov one, especially at high spins. {copyright} {ital 1996 The American Physical Society.}