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The q-analogue of the SU(2)-algebra, namely SU,(2), is applied to the description of the energy spectra of the deformed even-even nuclei. The theoretical results are compared with the available experimental data.

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An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.

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A collective vector-boson model with broken SU(3) symmetry, in which the ground state band and the lowest γ band belong to the same irreducible representation but are non-degenerate, is applied to several deformed even-even nuclei. The model description of ground and γ bands together with the corresponding B(E2) transition probabilities is investigated within a broad range of SU(3) irreducible representations (λ, µ). The calculations show that the (λ, µ) characteristics of rotational nuclei depend to a great extent on the magnitude of the SU(3) splitting between the ground and γ bands. It is found that for weakly split spectra, the ground-γ band coupling scheme is realized relevantly within narrow regions of "favored" (λ, µ) multiplets, while in the cases of strong splitting a description in which the ground band is situated alone in an irreducible representation is favored. The obtained results are analyzed in terms of the bandmixing interactions. The possibility for a transition between the different collective SU(3) schemes is discussed.