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.

In studying physics, it is important to solve problems with different methods and compare current and final results, which allows more comprehensive and deep analysis of the observed processes. In this paper, at a level of school physics course, the application of the principle of virtual work is presented as an alternative to the standard method for solving problems of statics. Two approaches are used to analyse two problems, as a result of which, without the use of integral calculus, formulas for the centres of mass of a circular arc and a circular sector are obtained.

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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.

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