Emergence of Euclidean dynamical symmetry as a consequence of shape phase mixing

A hybrid model which combines γ-stable and γ  -rigid collective conditions through a rigidity parameter, is used to study the critical point of the phase transition between spherical and axially symmetric shapes. The model in the equally mixed case, called X(4)X(4), exhibits properties of the Euclidean symmetry in four dimensions. The spectral properties of the new model are investigated in connection to the exact symmetry. Experimental realisation of the X(4)X(4) model is found in two N=90N=90 nuclei and two Pt isotopes in vicinity of experimentally observed critical point.