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

Model test of boson mappings

P. Navrátil, Jan Dobeš

Published Jul 1, 1992• 2 citations
Publisher

Abstract

Methods of boson mapping are tested in calculations for a simple model system of four protons and four neutrons in single-j distinguishable orbits. Two-body terms in the boson images of the fermion operators are considered. Effects of the seniority v=4 states are thus included. The treatment of unphysical states and the influence of boson space truncation are particularly studied. Both the Dyson boson mapping and the seniority boson mapping as dictated by the similarity transformed Dyson mapping do not seem to be simply amenable to truncation. This situation improves when the one-body form of the seniority image of the quadrupole operator is employed. Truncation of the boson space is addressed by using the effective operator theory with a notable improvement of results.

DOI
10.1103/physrevc.46.220

Related papers

Model calculations using boson mappings

P. Navrátil, J. Dobe

The shell-model fermion problem for systems of four protons and four neutrons in single-j shells is transformed into a boson problem using the generalized Dyson boson mapping. Exact boson calculations are performed. The spectrum of physical and nonphysical boson states and the effect of truncation in the boson space are studied. The necessity of transformation from the Dyson boson description to the seniority boson description is demonstrated within the truncated space.

Physical Review C•Nov 1, 1989•5 citations

Seniority mapping of single fermion operators

H. B. Geyer, Iain Morrison

We discuss the construction of ideal space seniority images of single fermion operators which proceeds via the generalized Dyson mapping and a subsequent similarity transformation. Particular attention is paid to the implications of a consistent treatment of single-particle and collective degrees of freedom. The results are compared with expressions for the mapped single fermion operators previously obtained, respectively, within the Otsuka-Arima-Iachello framework and by using the prescriptions of nuclear field theory. We point out certain inconsistencies in existing constructions of interacting-boson-fermion model operators in general and the interacting-boson-fermion model quadrupole operator in particular.

Physical Review C•Nov 1, 1989•9 citations

Microscopic Foundations of the Interacting Boson Model from the Shell-Model Point of View

Naotaka Yoshinaga, T. Mizusaki, Akito Arima +1 more

The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson sys­ tems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.

Progress of Theoretical Physics Supplement•Jan 1, 1996•50 citations

Microscopic Foundations of the Interacting Boson Model from the Shell-Model Point of View

Naotaka Yoshinaga, T. Mizusaki, A. Arima +1 more

The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson systems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.

Progress of Theoretical Physics Supplement•May 16, 2013•1 citation

Six-fermion tests of Dyson boson mappings

C. Martin Vincent, L. J. Henry, G.-K. Kim

Dyson mapping is directly applied to J=0 states of a system of six fermions in a single-j shell. It is found that the quality of the wave functions is drastically reduced when bosons of higher angular momentum are omitted. Nevertheless, a truncated Dyson boson method of calculating energies is explored.

Physical Review C•Apr 1, 1989•7 citations

Inadequacy of four-particle tests of Dyson boson mapping

G.-K. Kim, C. Martin Vincent

The spurious state problem is generalized Dyson boson mapping is examined. For cases where the fermion space is restricted to at most four-quasiparticle excitations, we show that Dyson boson images of normal-ordered quasiparticle interactions have identically vanishing matrix elements in the unphysical boson space. This ``decoupling'' feature explains the finding of previous authors that, in systems with at most four quasiparticles, every spurious state appears at its unperturbed energy. However, we show that the decoupling property does not generally hold in problems where there are excitations of more than four quasiparticles. Claims about methods for the spurious state problem, even though verified in four-quasiparticle calculations, may therefore be of limited validity.

Physical Review C•Nov 1, 1985•8 citations
Methods of boson mapping are tested in calculations for a simple model system of four protons and four neutrons in single-j distinguishable orbits. Two-body terms in the boson images of the fermion operators are considered. Effects of the seniority v=4 states are thus included. The treatment of unphysical states and the influence of boson space truncation are particularly studied. Both the Dyson boson mapping and the seniority boson mapping as dictated by the similarity transformed Dyson mapping do not seem to be simply amenable to truncation. This situation improves when the one-body form of the seniority image of the quadrupole operator is employed. Truncation of the boson space is addressed by using the effective operator theory with a notable improvement of results.
We discuss the construction of ideal space seniority images of single fermion operators which proceeds via the generalized Dyson mapping and a subsequent similarity transformation. Particular attention is paid to the implications of a consistent treatment of single-particle and collective degrees of freedom. The results are compared with expressions for the mapped single fermion operators previously obtained, respectively, within the Otsuka-Arima-Iachello framework and by using the prescriptions of nuclear field theory. We point out certain inconsistencies in existing constructions of interacting-boson-fermion model operators in general and the interacting-boson-fermion model quadrupole operator in particular.
The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson sys­ tems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.
The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson systems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.
The spurious state problem is generalized Dyson boson mapping is examined. For cases where the fermion space is restricted to at most four-quasiparticle excitations, we show that Dyson boson images of normal-ordered quasiparticle interactions have identically vanishing matrix elements in the unphysical boson space. This ``decoupling'' feature explains the finding of previous authors that, in systems with at most four quasiparticles, every spurious state appears at its unperturbed energy. However, we show that the decoupling property does not generally hold in problems where there are excitations of more than four quasiparticles. Claims about methods for the spurious state problem, even though verified in four-quasiparticle calculations, may therefore be of limited validity.