Regularities of low-lying states with random interactions in the fermion dynamical symmetry model

Abstract

In this paper we study low-lying states under random interactions in the framework of the fermion dynamical symmetry model (FDSM), regardless of the ground state spin. Very strong correlations are found for ${R}_{6}$ versus ${R}_{4}$ (where ${R}_{I}\ensuremath{\equiv}{E}_{{I}_{1}^{+}}/{E}_{{2}_{1}^{+}})$ for the entire ensemble. We present arguments on the origin of these regular patterns in terms of the dynamical symmetries of the FDSM. The regular patterns of $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ versus $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ are found.