Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry

Abstract

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.

arXiv comment16 pages, 1 figure, 10 tables

References in corpus (14)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Construction of high-quality Nucleon-Nucleon potential models
• Theoretical Foundation of the Nuclear Force in QCD and its applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
• Probing the core of the strong nuclear interaction
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Proxy-SU(3) symmetry in heavy deformed nuclei
• Proxy-SU(3) symmetry in the shell model basis
• Prolate over oblate dominance in deformed nuclei as a consequence of the SU(3) symmetry and the Pauli principle
• Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator
• Parameter-free predictions for the collective deformation variables beta and gamma within the pseudo-SU(3) scheme
• Shape Deformations in Atomic Nuclei
• The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters

Cited by in corpus (6)

• Shape coexistence in even-even nuclei: A theoretical overview
• The proxy-SU(3) symmetry in atomic nuclei
• Islands of shape coexistence: theoretical predictions and experimental evidence
• Microscopic origin of shape coexistence in the N=90, Z=64 region
• Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems
• Shell-model description of collective deformation variables $\beta$ and $\gamma$ in ${}^{164-188}$Hf nuclei