Proxy-SU(3) symmetry in the shell model basis

Abstract

The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit--Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.

arXiv comment15 pages, 7 tables, 1 figure

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• Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
• Signatures for shape coexistence and shape/phase transitions in even-even nuclei
• Islands of shape coexistence: theoretical predictions and experimental evidence
• Microscopic origin of shape coexistence in the N=90, Z=64 region
• Single-particle and collective structures in neutron-rich Sr isotopes
• SU(3)-guided Realistic Nucleon-nucleon Interactions for Large-scale Calculations
• Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems
• Inter-band B(E1) Strengths in Heavy Nuclei based on the Proxy-SU(3) Scheme