The collective Hamiltonian including isovector pairing and [Formula: see text]-particle-type correlation degrees of freedom is constructed. The Hamiltonian is applied to description of the relative energies of the ground states of even–even nuclei around [Formula: see text]Ni. A satisfactory description of the experimental data is obtained. A significant improvement of the agreement with the experimental data compared to our previous calculations is explained by inclusion in the Hamiltonian of the dynamical variables describing [Formula: see text]-particle-type correlations.

Рассмотрены примеры фазовых переходов в атомных ядрах, идущих при увеличении энергии возбуждения, углового момента и изменении числа нуклонов. Продемонстрирована возможность описания этих переходов в рамках коллективных моделей с гамильтонианом, зависящим от небольшого числа динамических переменных.

Examples of phase transitions occurring in atomic nuclei in response to an increase in the excitation energy and angular momenta and in response to a change in the number of nucleons are considered. The possibility of describing such transitions within collective models based on a Hamiltonian that depends on a relatively small number of dynamical variables is demonstrated.

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 observed properties of the low-lying collective excitations of 96Zr and 96Mo are investigated in the framework of the collective quadrupole nuclear model with the Bohr Hamiltonian, whose potential energy has two minima – spherical and deformed. Satisfactory description of the excitation energies and E2 transition probabilities is obtained. It is shown that in the case of 96Zr both minima are sufficiently deep. However, in the case of 96Mo a deformed minimum is only outlined.

Experimental data on Zr-96 indicate coexisting spherical and deformed structures with small mixing amplitudes. Although a possible geometrical description of such a shape coexistence is implied in the contemporary discussion, it does not exist yet for Zr-96. The observed properties of the low-lying collective states of Zr-96 based on the geometrical collective model are investigated. The quadrupole-collective Bohr Hamiltonian with the potential having two minima, spherical and deformed, is applied. Good agreement with the experimental data on the excitation energies, B(E2), and B(M1) reduced transition probabilities is obtained. It is shown that the low-energy structure of Zr-96 can be described in a satisfactory way within the geometrical collective model with a potential function supporting shape coexistence without other restrictions of its shape. However, the excitation energy of the 2(2)(+) state can be reproduced only if the rotation inertia coefficient is taken to be 5 times smaller than the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of B(M1; 2(2)(+) -> 2(1)(+)). An indication of the influence of the pairing vibrational mode on the 0(2)(+) -> 0(1)(+) transition is obtained.

The energy as determined experimentally for the first excited 2+ state of the 156Gd rotational band based on the mixed-symmetry state is extremely small in relation to characteristic values of this energy in deformed nuclei. The possibility of explaining this experimental fact by a large value of the decoupling parameter is explored. The result is that the decoupling-parameter values obtained under various assumptions on the structure of the mixed-symmetry state are too small for explaining the experimental excitation energy of the state in question.

We propose a theoretical approach to the consideration of the Hamiltonian with pairing forces using the technique of finite boson representation. We show that a simultaneous description of the pairing vibrational state in 56Ni and the pairing rotational states with the isospin $ 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 obtained from 56Ni by adding (removing) 12 or more nucleons exceed significantly the experimental values. A possible reason for this discrepancy is discussed.