Dynamical Symmetries in Shell and Collective Models of Nuclear Structure
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ynamical Symmetries in Shell and Collective Models of Nuclear Structure A. I. Georgievaa, *, K. P. Drumevb, and V. P. Garistovb aInstitute
for Climate, Atmosphere and Water Research, Bulgarian Academy of Sciences, Sofia, BG-1784 Bulgaria of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, BG-1784 Bulgaria *e-mail: [email protected]
bInstitute
Received March 2, 2020; revised April 15, 2020; accepted April 27, 2020
Abstract—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. DOI: 10.3103/S1062873820080134
INTRODUCTION Symmetry-adapted nuclear models [1] are a useful tool to explore nuclear systems. Usually, these kinds of models have a few dynamical symmetries, which give analytical solution and are considered as limiting cases. But in real nuclei they may be simultaneously present and compete. Hence, it is a challenging problem to explore the contribution of each of these simple limits into the resulting realistic behavior of the system. A fundamental illustration of such an approach is presented by the algebraic structure of the shell model, realized in terms of fermion creation and annihilation operators. In this case, the long-range quadrupolequadrupole interaction competes with different types of short-range pairing interactions. The investigations of the possible dynamical symmetries in the microscopic Pairing-plus-Quadrupole Shell Model (PQM) [2], led to establishing important connections between the groups generating the Hamiltonian of the model. These connections simplified the description of the influence of the different interactions on the energy spectra and transitions in realistic nuclei. It is another challenge for the theoretical models to achieve a correct interpretation of the data on the observed collective states as they are well organized in bands, revealing their structure and origin. Boson algebraic models play an im
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