The dynamical symmetries in the algebraic shell model and the collective Interacting Vector Boson Model (IVBM) realized in terms of fermion and boson creation and annihilation operators are investigated. The obtained analytic eigen-energies in both models are compared with the experimental ones and the strengths of the corresponding terms of the model Hamiltonians are evaluated in both cases. In the algebraic realization of the Pairing plus Quadrupole Shell Model the correlations and transition between the quadrupole and pairing phases—dynamical symmetries are investigated in application to nuclear systems in the first few light shells. In the symplectic extension of the IVBM the spectra of heavy even-even nuclei with transitional between rotational and vibrational character is well reproduced. The algebraic connections between dynamical symmetries of the nuclear collective spectra and the ordering of the low-lying states with fixed angular momentum permits a reasonable and experimentally proved prediction of the position of the 0+ band heads of the collective bands. The models based on dynamical symmetries give an elegant and simple way to describe the complex spectra of nuclei with different shapes.
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Georgieva, A.I., Drumev, K.P. & Garistov, V.P. Dynamical Symmetries in Shell and Collective Models of Nuclear Structure. Bull. Russ. Acad. Sci. Phys. 84, 1027–1033 (2020). https://doi.org/10.3103/S1062873820080134