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

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