Low-lying collective excitations of nuclei are described in the SD-pair shell approach. To facilitate the computational difficulties the Hilbert space cutoff is performed up to SD-pair, in which a microscopic justification of the model of interacting bosons is given. The diagonalization of the fermionic Hamiltonian in the cutoff space is applied to the study of the spectra structure and reduced probabilities of the electromagnetic transitions B (E2) in the spherical isotopes of Ruthenium with the atomic weight A = 100,102,104. These values are compared with their experimental data.

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The processes of interaction of alpha particles with collective states of nuclei Mg Ne 24 22 , by strongly-connected channels of nuclear reactions studied. As the collective Hamiltonian able to take the expression patterns of the interacting bosons model (IBM).