Correlations of the <em>SO</em>(8) Pairing and <em>SU</em>(3) Quadrupole Bases in the Algebraic Shell Model

Ana Ivanova Georgieva; Kalin Pavlov Drumev

doi:10.11804/NuclPhysRev.34.01.062

We establish a correspondence between the SO(8) isoscalar, isovector and total pairing bases and the Elliott's SU(3) basis in the algebraic structure of the spatial part of the microscopic shell model. It is derived from the complementarity of these algebras to the same T, S, (S,T) irreducible representations (irreps) of the Wigners supermultiplets, contained in the shell-model number-conserving algebra U(4Ω). This important result allows for the evaluation of the content of SU(3) irreps into the different types of pairing bases which leads to an investigation of the complementarity and competitive effects of pairing and the quadrupole-quadrupole interactions on the energy spectra of the nuclear systems. The theory is valid for any shell and for a number of shells as well, but we illustrate it with the results for a single ds-shell.

Correlations of the SO(8) Pairing and SU(3) Quadrupole Bases in the Algebraic Shell Model

1. Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria;

2. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria

Funds: Bulgarian National Foundation for Scientific Research(DFNI-E02/6/12.12.2014)

Received Date: 2016-09-18

Publish Date: 2017-03-20

Key words:

Abstract: We establish a correspondence between the SO(8) isoscalar, isovector and total pairing bases and the Elliott's SU(3) basis in the algebraic structure of the spatial part of the microscopic shell model. It is derived from the complementarity of these algebras to the same T, S, (S,T) irreducible representations (irreps) of the Wigners supermultiplets, contained in the shell-model number-conserving algebra U(4Ω). This important result allows for the evaluation of the content of SU(3) irreps into the different types of pairing bases which leads to an investigation of the complementarity and competitive effects of pairing and the quadrupole-quadrupole interactions on the energy spectra of the nuclear systems. The theory is valid for any shell and for a number of shells as well, but we illustrate it with the results for a single ds-shell.

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Correlations of the SO(8) Pairing and SU(3) Quadrupole Bases in the Algebraic Shell Model

doi: 10.11804/NuclPhysRev.34.01.062

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Correlations of the SO(8) Pairing and SU(3) Quadrupole Bases in the Algebraic Shell Model

doi: 10.11804/NuclPhysRev.34.01.062

1. Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria;

2. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria

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Correlations of the SO(8) Pairing and SU(3) Quadrupole Bases in the Algebraic Shell Model

doi: 10.11804/NuclPhysRev.34.01.062

Abstract

References

Proportional views

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Correlations of the SO(8) Pairing and SU(3) Quadrupole Bases in the Algebraic Shell Model

doi: 10.11804/NuclPhysRev.34.01.062

1. Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria; 2. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria

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1. Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria;

2. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria