On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method

Egido, J.L.; Lessing, J.; Martín, Vicente; Robledo, L. M.

doi:10.1016/0375-9474(95)00370-g

Cited by 78 publications

(81 citation statements)

References 6 publications

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“…The triaxial calculations are more involved than the axial ones (computationally, around a factor 60 more expensive) and this fact restricts them to relevant candidates only. In both types of calculations, axial and triaxial, the solution of the HFB equations has been reformulated as a minimization process and the so-called gradient method [27] has been used to locate the minimum. The gradient method has the advantage over the usual way of solving the HFB Potential energy curves obtained with the Gogny D1S force (full lines) for the isotopes of Pd.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Evolution of nuclear shapes in medium mass isotopes from a microscopic perspective

2008

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The self-consistent Hartree-Fock-Bogoliubov approximation based on the finite-range and density-dependent Gogny interaction (parametrization D1S) has been used to generate potential energy curves in various chains of Pd, Xe, Ba, Nd, Sm, Gd, and Dy isotopes. The evolution of shapes with the number of nucleons is studied and a search for signatures of E(5) and X(5) critical point symmetries is also conducted. The results are compared with those obtained in the framework of other mean-field approximations to the nuclear many-body problem. The role of triaxiality in nuclei where this degree of freedom could be relevant is considered and discussed.

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Section: Theoretical Frameworkmentioning

confidence: 99%

Evolution of nuclear shapes in medium mass isotopes from a microscopic perspective

2008

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“…The corresponding equations have been solved by the Conjugate Gradient Method [12]. The Bogoliubov transformation (1) leads to wave functions |Φ that are not eigenstates of the particle number operator.…”

Section: Theorymentioning

confidence: 99%

Coulomb exchange and pairing contributions in nuclear Hartree–Fock–Bogoliubov calculations with the Gogny force

2001

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We present exact Hartree-Fock-Bogoliubov calculations with the finite range density dependent Gogny force using a triaxial basis. For the first time, all contributions to the Pairing and Fock Fields arising from the Gogny and Coulomb interactions as well as the two-body correction of the kinetic energy have been calculated in this basis. We analyze the relevance of these terms in different regions of the periodic table at zero and high angular momentum. The validity of commonly used approximations that neglect different terms in the variational equations is also checked. We find a decrease of the proton pairing energies mainly due to a Coulomb antipairing effect.

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“…Here the indices (µ, ν) run over the proton and neutron configuration space. The solution of the projected variational problem can be obtained by the conjugate gradient method [16].…”

Section: Prescription 2: Mixed Densitymentioning

confidence: 99%

Particle number projection with effective forces

2001

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The particle number projection method is formulated for density dependent forces and in particular for the finite range Gogny force. Detailed formula for the projected energy and its gradient are provided. The problems arising from the neglection of any exchange term, which may lead to divergences, are thoroughly discussed and the possible inaccuracies estimated. Numerical results for the projection after variation method are shown for the nucleus 164 Er and for the projection before variation approach for the nuclei 48,50 Cr. We also confirm the Coulomb antipairing effect found in mean field theories.

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On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method

Cited by 78 publications

References 6 publications

Evolution of nuclear shapes in medium mass isotopes from a microscopic perspective

Evolution of nuclear shapes in medium mass isotopes from a microscopic perspective

Coulomb exchange and pairing contributions in nuclear Hartree–Fock–Bogoliubov calculations with the Gogny force

Particle number projection with effective forces

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