Hidden Euclidean Dynamical Symmetry in the U(n + 1) Vibron Model

Abstract

Based on the boson realization of the Euclidean algebras, it is found that the E(n) dynamical symmetry (DS) may emerge at the critical point of the U(n)-SO(n+1) quantum phase transition. To justify this finding, we provide a detailed analysis of the transitional Hamiltonian in the U(n+1) vibron model in both quantal and classical ways. It is further shown that the low-lying structure of 82Kr can serve as an excellent empirical realization of the E(5) DS, which provides a specific example of the Euclidean DS in experiments.