Effects of beta-gamma coupling in transitional nuclei and the validity of the approximate separation of variables

Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a beta-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong beta-gamma coupling effects. The validity of the approximate separation of variables introduced with the X(5) model, extensively applied in recent analyses of axially stabilized transitional nuclei, is examined, and the reasons for its breakdown are analyzed.