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The low-lying collective properties of ¹⁰²Pd, ¹⁰⁶Cd, ¹²⁴Te and ¹²⁸Xe nuclei have been established. The relation between gamma-energy over spin E_γ/I as a function of spin I has been drawn to determine the properties of these nuclei in the ground states band. The combined vibrator-γ-soft energy equation was used to calculate the energy of the ground states band for the above nuclei, and it was compared with the calculated energy by using the U(5)–O(6) of the IBM-1. The calculation of the combined equation and the IBM-1 is in good agreement with the measured and other calculated values.

A description of the even–even Pt isotopes for A = 190 to 196 in the framework of the Interacting Boson Model (IBM-1) is carried out. Energy levels, B(E2) and B(M1) values, branching ratios, E2/M1 mixing ratios and Q_J values of the above nuclei have been calculated. The energy levels, B(E2) values and the electric quadrupole moment Q_J results are reasonably consistent with the experimental data. The magnetic dipole is compared with the available experimental data. Furthermore, the calculated results are better than previous studies.

The phenomenological classification of collective quadrupole excitations by means of the Bohr–Hamiltonian (BH) is reviewed with focus on signatures for triaxility. The variants of the microscopic BH derived by means of the Adiabatic Time-Dependent Mean Field theory from the Pairing-plus-quadrupole–quadrupole interaction, the Shell Correction Method, the Skyrme Energy Density Functional, the Relativistic Mean Field Theory and the Gogny interaction are discussed and applications to concrete nuclides reviewed. The Generator Coordinate Method for the five-dimensional quadrupole deformation space and first applications to triaxial nuclei are presented. The phenomenological classification in the framework of the Interacting Boson Model is discussed with a critical view on the boson number counting rule. The recent success in calculating the model parameters by mapping the mean field deformation energy surface on the bosonic one is discussed and the applications listed. A critical assessment of the models is given with focus on the limitations due to the adiabatic approximation. The Tidal Wave approach and the Triaxial Projected Shell Model are presented as practical approaches to calculate spectral properties outside the adiabatic region.

In this paper, the interacting boson model (IBM-1) with intrinsic coherent state is used to study the O(6) shapes in Se isotopes. The Hamiltonian is written in the annihilation and creation form with one and two body terms. For each nucleus, a fitting procedure is adopted to get the best model parameters by fitting selected experimental energy levels, B(E2), B(M1) transition rates and mixing ratio with the calculated ones. The O(6) IBM potential energy surfaces (PESs) are analyzed.