https://doi.org/10.1140/epja/s10050-021-00395-x
Review
Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
1
Institute of Nuclear and Particle Physics, National Centre of Scientific Research “Demokritos”, Aghia Paraskevi, 15310, Attiki, Greece
2
Department of Physics, Faculty of Science, University of Zagreb, 10000, Zagreb, Croatia
3
Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, 1784, Sofia, Bulgaria
Received:
22
December
2020
Accepted:
1
February
2021
Published online:
2
March
2021
The consequences of the attractive, short-range nucleon–nucleon (NN) interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3) symmetry are discussed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation, which corresponds to the maximal spatial overlap among the fermions. The percentage of the symmetric components out of the total in an SU(3) wave function is introduced, through which it is found, that no SU(3) irrep is more symmetric than the highest weight irrep for a certain number of valence particles in a three dimensional, isotropic, harmonic oscillator shell. The consideration of the highest weight irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid-shell region
This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning 2014-2020” in the context of the project “Nucleon Separation Energies” (MIS 5047793)
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
