Within the framework of a model based on the Bohr Hamiltonian, the properties of low-lying collective states of ⁹²⁻¹⁰²Zr are investigated. It is shown that the experimental excitation energies and the reduced probabilities of the E2 and M1 transitions are satisfactorily described by assuming the coexistence of two potential energy minima. The simultaneous formation of spherical and deformed minima indicates the shape coexistence phenomenon in these nuclei.

A model of octupole vibrations is proposed that allows one to obtain analytical expressions for the dependences of the parity splitting and E1 transitional moment in alternating parity bands on the angular momentum of the nucleus. The key parameter in these expressions is the critical angular momentum determining the transition from octupole vibrations to stable octupole deformation. The spectra of alternating parity bands and E1 transition probabilities in actinides and rare-earth nuclei are described.

Using the results of the DNS cluster model, the energies of the lowest states of negative parity and the reduced probabilities of E1 and E3 transitions from these states to the ground states for superheavy nuclei with Z > 96 are predicted.

(based on the Ph.D. thesis)