Random interactions in nuclei and extension of $0^{+}$ dominance in ground states to irreps of group symmetries

Abstract

Random one plus two-body hamiltonians invariant with respect to $O({\mathcal{N}}_1)\oplus O({\mathcal{N}}_2)$ symmetry in the group-subgroup chains $U(\mathcal{N})\supset U({\mathcal{N}}_1)\oplus U({\mathcal{N}}_2)\supset O({\mathcal{N}}_1)\oplus O({\mathcal{N}}_2)$ and $U(\mathcal{N})\supset O(\mathcal{N})\supset O({\mathcal{N}}_1)\oplus O({\mathcal{N}}_2)$ chains of a variety of interacting boson models are used to investigate the probability of occurrence of a given $({\omega }_1{\omega }_2)$ irreducible representation (irrep) to be the ground state in even-even nuclei; $[{\omega }_1]$ and $[{\omega }_2]$ are symmetric irreps of $O({\mathcal{N}}_1)$ and $O({\mathcal{N}}_2)$ respectively. Numerical results obtained for ${\mathcal{N}}_1\ge 3,{\mathcal{N}}_2=1$ and ${\mathcal{N}}_1,{\mathcal{N}}_2\ge 3$ situations are well explained by an extended Hartree-Bose mean-field analysis.

8 pages, 1 figure