Background: Experimental data on 96 Zr indicate coexisting spherical and deformed structures with small mixing amplitudes.Purpose: To investigate the properties of the low-lying collective states of 96 Zr based on the collective quadrupole Bohr Hamiltonian.Method: The β-dependent collective potential having two minima -spherical and deformed, is fixed so to describe experimental data in the best way.Results: Good agreement with the experimental data on the excitation energies, B(E2) and B(M 1) reduced transition probabilities is obtained.Conclusion: It is shown that the low-energy structure of 96 Zr can be reproduced in a satisfactory way in the geometrical model with a potential function supporting shape coexistence. However, the excitation energy of the 2 + 2 state can be reproduced only if the rotation inertia coefficient is taken five times smaller then the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the B(M 1; 2 + 2 → 2 + 1 ) value. An indication on the influence of the pairing vibrational mode on the ρ 2 (0 + 2 → 0 + 1 ) value is obtained.

The eigensolutions of the collective Hamiltonian with different potentials suggested for description of the isovector pair correlations are obtained, analyzed and compared with the experimental energies. It is shown that the isovector pair correlations in nuclei around [Formula: see text]Ni can be described as anharmonic pairing vibrations. The results obtained indicate the presence of the [Formula: see text]-particle type correlations in these nuclei and the existence of the interaction different from isovector pairing which also influences on the isospin dependence of the energies.

The theoretical approach to consideration of the Hamiltonian with pairing forces using a technique of the finite boson representation is developed. It is shown that a simultaneous description of the pairing vibrational state in 56 Ni and the pairing rotational states with T =0 in the neighboring N = Z nuclei is possible if the pairing Hamiltonian takes into account only isovector monopole pairing. However, the calculated energies of the pairing rotational states of N = Z nuclei removed from 56 Ni by 12 and more nucleons exceed significantly the experimental values. The possible reason of this discrepancy is discussed.