Evolution of collectivity in even-even transitional nuclei with the particle number

The low-lying excited states in even-even nuclei with nucleons outside of the closed shells are often described in the framework of the Bohr-Mottelson (BM) collective model as vibrational or rotational states. In reality this picture is too simplified since most of the even-even nuclei exhibit features between these two limiting cases. It was suggested that interplay between rotational and vibrational motion has to be accounted. In 1958 and 1956 two collective models were developed - the triaxial model of Davydov and Filippov and the gamma-unstable rotor of Wilets and Jean, which allowed to distinguish some nuclei with particular transitional features between vibrational and rotational behaviour. The first one represents the solution of the problem for rotating triaxial rotor, while the second one gives an exact solution of the BM Hamiltonian with γ-independent potential. The interest in the exact solutions of BM Hamiltonian has been recently renewed. It was suggested that in the nature there are some nuclei with particular shapes corresponding to analytical solutions of the BM Hamiltonian, while the rest of the nuclei have transitional (shape "phases") behaviour. The theoretical breakthrough in the exact solutions of the BM Hamiltonian entails a number of experiments in which the nuclei with spectra similar to the "symmetrical" solutions of BM Hamiltonian are searched.