Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

Abstract

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of nuclear models bearing the SU(3) symmetry are reviewed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation (irrep), which corresponds to the maximal spatial overlap among the fermions. The consideration of the highest weight (hw) irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid-shell region. Subsequently, the consequences of the use of the hw irreps on the binding energies and two-neutron separation energies in the rare earth region are discussed within the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing only the three dimensional (3D) isotropic harmonic oscillator (HO) term and the quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3) symmetry and treats the nucleus as a rigid rotator.

arXiv comment6 pages, 4 figures, to appear in HINP 6th International Workshop; Perspectives on Nuclear Physics: from Fundamentals to Applications (online, May 14-16, 2021)

References in corpus (7)

• Pseudo-spin as a Relativistic Symmetry
• Spherical Shell Model description of rotational motion
• 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
• Parameter-free predictions for the collective deformation variables beta and gamma within the pseudo-SU(3) scheme
• Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
• Shape Deformations in Atomic Nuclei