Abstract
This chapter discusses symmetry methods as used in models of atomic nuclei. After an introduction of the notions of dynamical algebra, symmetry algebra, and dynamical symmetry, relevant to any quantum many-body system, the focus is on a few historical models of seminal importance to our understanding of the structure of nuclei. They include the quasi-spin SU(2) model of pairing [and its neutron-proton SO(8) generalization], the SU(4) supermultiplet model, the SU(3) model of deformed nuclei, and the U(6) interacting boson model of collective nuclear excitations. The guiding thread of this review is that all these models can be understood from a common perspective based on the analysis of their symmetry character, which unveils the solvability of classes of model Hamiltonians and enables to establish connections between the single-particle and collective descriptions of nuclei.
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Isacker, P.V. (2022). Algebraic Models of Nuclei. In: Tanihata, I., Toki, H., Kajino, T. (eds) Handbook of Nuclear Physics . Springer, Singapore. https://doi.org/10.1007/978-981-15-8818-1_13-1
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