Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review C

Solvable many-level pairing model in a boson formalism

D. Gambacurta, Michelangelo Sambataro, F. Catara

Published Jan 26, 2006• 7 citations
Publisher

Abstract

We analyze an exactly solvable many-level pairing model (the picket-fence model) in a boson formalism. By making use of a Marumori-type mapping procedure, we construct a boson image of the model Hamiltonian. Only two- and four-boson operators are included in the boson expansion. We show that the physical spectrum of this Hamiltonian coincides with the exact one, and, in particular, we recover Richardson's equations. We apply this boson formalism to search for possible extensions of the random-phase approximation (RPA). We construct renormalized RPA-type equations in correspondence with different expansions of the boson operators. We discuss two extensions of the RPA and test them by comparing their predictions with the exact results and with those obtained within the RPA and the self-consistent RPA.

DOI
10.1103/physrevc.73.014310

Related papers

Bosonic Treatment of Pairing Correlations in a Solvable Many-Level Model

D. Gambacurta

We discuss two extensions of RPA based on a boson formalism and report on some applications within an exactly solvable many‐level pairing model. By making use of a Marumori‐type mapping procedure, we preliminary define the boson image of the fermion operators of interest and, in particular, of the model Hamiltonian. This includes two and four‐boson terms. We therefore construct renormalized RPA‐type equations in correspondence with different expansions of the boson operators. The approximate calculations are compared with the exact ones and with those obtained within RPA and Self Consistent RPA. We find that it is possible to improve considerably upon RPA by still keeping the formalism simple enough to be applied in more realistic cases without a too serious computational effort.

AIP conference proceedings•Jan 1, 2005•0 citations

Extended RPA within a solvable 3 level model

F. Catara, M. Grasso, Michelangelo Sambataro

Working within an exactly solvable 3 level model, we discuss am extension of the Random Phase Approximation (RPA) based on a boson formalism. A boson Hamiltonian is defined via a mapping procedure and its expansion truncated at four-boson terms. RPA-type equations are then constructed and solved iteratively. The new solutions gain in stability with respect to the RPA ones. We perform diagonalizations of the boson Hamiltonian in spaces containing up to four-phonon components. Approximate spectra exhibit an improved quality with increasing the size of these multiphonon spaces. Special attention is addressed to the problem of the anharmonicity of the spectrum.

arXiv:nucl-th/0203029•Mar 13, 2002•0 citations

Boson-mapping-based extension of the random-phase approximation in a three-level Lipkin model

M. Grasso, F. Catara, Michelangelo Sambataro

Working within an exactly solvable three level model a boson Hamiltonian is defined via a mapping procedure and its expansion truncated at four-boson terms. The resulting spectrum is found in good agreement with the exact one. We discuss an extension of the random-phase approximation (RPA) based on this boson formalism. Nonlinear RPA-type equations are constructed and solved iteratively. The new solutions gain in stability with respect to the RPA ones. We perform diagonalizations of the boson Hamiltonian in restricted spaces; approximate spectra exhibit an improved quality with increasing the size of these spaces. Special attention is addressed to the problem of the anharmonicity of the spectrum.

Physical Review C•Dec 4, 2002•11 citations

The Pairing interaction in nuclei: comparison between exact and approximate treatments

J. Dukelsky, G.G. Dussel, Jorge G. Hirsch +1 more

As a model for a deformed nucleus the many level pairing model (picket fence model with ~100 levels) is considered in four approximations and compared to the exact solution given by Richardson long time ago. It is found that, as usual, the number projected BCS method improves over standard BCS but that it is much less accurate than the more sophisticated many-body-approaches which are Coupled Cluster Theory (CCT) in its SUB2 version or Self-Consistent Random Phase Approximation (SCRPA).

arXiv:nucl-th/0206016•Jun 6, 2002•0 citations

Variational approach to collective excitations

Michelangelo Sambataro, Nguyen Dinh Dang

We discuss a variational approach to collective excitations in a boson formalism based on quasiparticles. Bosons are defined in correspondence with pairs of quasiparticles and boson images of fermion operators are constructed by means of a mapping procedure of Marumori-type. Phonons of the type used within the random phase approximation (RPA) are introduced as Bogoliubov transformations of these bosons. The variables entering into the definition of these phonons as well as of the quasiparticle operators are fixed simultaneously by minimizing the expectation value of the boson Hamiltonian in the vacuum of the phonons. The approach is tested within an exactly solvable two-level model which is characterized by a pairing Hamiltonian. A quite good agreement is found for the energies of the ground state and of the first ${0}^{+}$ excited state. The comparison with the Bardeen-Cooper-Schrieffer method and the quasiparticle RPA as well as with some recent self-consistent RPA-type approaches is discussed.

Physical Review C•Mar 1, 1999•21 citations

Extended random-phase approximation in a boson formalism with Pauli principle

Michelangelo Sambataro, F. Catara

The random-phase approximation (RPA) is examined in a boson formalism and special attention is focused on the problem of the violation of the Pauli principle affecting this theory. A mapping technique is discussed and the boson image of a two-body fermion Hamiltonian is constructed. Within the boson space so defined, an extension of RPA is proposed where structure and energy of the ground state, as well as those of the one-phonon states, are analyzed with regard to the role of the spurious components associated with a violation of the Pauli principle. A multistep minimization procedure for the determination of a better ground state is also examined. Numerical tests are performed within the Lipkin-Meshkov-Glick model.

Physical Review C•Jun 1, 1995•14 citations
We analyze an exactly solvable many-level pairing model (the picket-fence model) in a boson formalism. By making use of a Marumori-type mapping procedure, we construct a boson image of the model Hamiltonian. Only two- and four-boson operators are included in the boson expansion. We show that the physical spectrum of this Hamiltonian coincides with the exact one, and, in particular, we recover Richardson's equations. We apply this boson formalism to search for possible extensions of the random-phase approximation (RPA). We construct renormalized RPA-type equations in correspondence with different expansions of the boson operators. We discuss two extensions of the RPA and test them by comparing their predictions with the exact results and with those obtained within the RPA and the self-consistent RPA.
We discuss two extensions of RPA based on a boson formalism and report on some applications within an exactly solvable many‐level pairing model. By making use of a Marumori‐type mapping procedure, we preliminary define the boson image of the fermion operators of interest and, in particular, of the model Hamiltonian. This includes two and four‐boson terms. We therefore construct renormalized RPA‐type equations in correspondence with different expansions of the boson operators. The approximate calculations are compared with the exact ones and with those obtained within RPA and Self Consistent RPA. We find that it is possible to improve considerably upon RPA by still keeping the formalism simple enough to be applied in more realistic cases without a too serious computational effort.
Working within an exactly solvable 3 level model, we discuss am extension of the Random Phase Approximation (RPA) based on a boson formalism. A boson Hamiltonian is defined via a mapping procedure and its expansion truncated at four-boson terms. RPA-type equations are then constructed and solved iteratively. The new solutions gain in stability with respect to the RPA ones. We perform diagonalizations of the boson Hamiltonian in spaces containing up to four-phonon components. Approximate spectra exhibit an improved quality with increasing the size of these multiphonon spaces. Special attention is addressed to the problem of the anharmonicity of the spectrum.
Working within an exactly solvable three level model a boson Hamiltonian is defined via a mapping procedure and its expansion truncated at four-boson terms. The resulting spectrum is found in good agreement with the exact one. We discuss an extension of the random-phase approximation (RPA) based on this boson formalism. Nonlinear RPA-type equations are constructed and solved iteratively. The new solutions gain in stability with respect to the RPA ones. We perform diagonalizations of the boson Hamiltonian in restricted spaces; approximate spectra exhibit an improved quality with increasing the size of these spaces. Special attention is addressed to the problem of the anharmonicity of the spectrum.
We discuss a variational approach to collective excitations in a boson formalism based on quasiparticles. Bosons are defined in correspondence with pairs of quasiparticles and boson images of fermion operators are constructed by means of a mapping procedure of Marumori-type. Phonons of the type used within the random phase approximation (RPA) are introduced as Bogoliubov transformations of these bosons. The variables entering into the definition of these phonons as well as of the quasiparticle operators are fixed simultaneously by minimizing the expectation value of the boson Hamiltonian in the vacuum of the phonons. The approach is tested within an exactly solvable two-level model which is characterized by a pairing Hamiltonian. A quite good agreement is found for the energies of the ground state and of the first 0+{0}^{+}0+ excited state. The comparison with the Bardeen-Cooper-Schrieffer method and the quasiparticle RPA as well as with some recent self-consistent RPA-type approaches is discussed.
The random-phase approximation (RPA) is examined in a boson formalism and special attention is focused on the problem of the violation of the Pauli principle affecting this theory. A mapping technique is discussed and the boson image of a two-body fermion Hamiltonian is constructed. Within the boson space so defined, an extension of RPA is proposed where structure and energy of the ground state, as well as those of the one-phonon states, are analyzed with regard to the role of the spurious components associated with a violation of the Pauli principle. A multistep minimization procedure for the determination of a better ground state is also examined. Numerical tests are performed within the Lipkin-Meshkov-Glick model.