Eur. Phys. J. A (2020) 56: 239
https://doi.org/10.1140/epja/s10050-020-00239-0

Review

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

¹ Institute of Nuclear and Particle Physics, National Centre of Scientific Research “Demokritos”, Aghia Paraskevi, 15310, Attiki, Greece
² Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, 1784, Sofia, Bulgaria
³ Institute for Nuclear Research, Pf. 51, Debrecen, 4001, Hungary

^* e-mail: martinou@inp.demokritos.gr

Received: 8 July 2020
Accepted: 30 August 2020
Published online: 26 September 2020

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.