Nuclear supersymmetry and dual algebraic structures

Abstract

Superalgebras and supersymmetries are relevant to mixed systems of bosons and fermions. A simple systematic procedure to construct the multi-level unitary and orthosymplectic superalgebras which appear in the generalized multi-level pairing models and for arbitrary choice of level degeneracies is presented. The algebraic substructures of these superalgebras are discussed and the explicit formulae for their generators and Casimir operators are given in spherical tensor (Racah) form. We draw attention to the existence of four general types of dynamical supersymmetry, including two vibrational limits and two γ-unstable limits. Their analytical expressions of the energies are derived. The relations between pairing operators and the multipole operators for the supersymmetric multi-level system are given in a closed form. The results presented show very clearly the duality between the orthosymplectic superalgebras and the generalized quasi-spin algebras for the supersymmetric system with pairing interactions. Using the concept of complementary subalgebras, the full super two-level pairing Hamiltonian, with uniform pairing strength, and the dynamical symmetries are rewritten, in a more convenient form. The generalization of the class C transitional Hamiltonian is demonstrated.

Coexistence and fluctuations phenomena with Davidson-like potentials in quadrupole–octupole deformed nuclei

“…In nuclear physics, the quantum shape-phase transition (QSPT) has received much interest in recent decades [1][2][3][4][5][6][7][8][9][10][11][12]. QSPTs are abrupt changes within the structure of the energy spectrum, caused by a change in the parameters of the quantum Hamiltonian.…”

“…QSPTs are abrupt changes within the structure of the energy spectrum, caused by a change in the parameters of the quantum Hamiltonian. With QSPT, the concept critical point [3][4][5][6][7][8], based on very simple shaped potentials, describes the dynamical symmetry of the nuclear system at points of QSPT between various phases. Up to now, the studies based on these potentials concentrate on the studying of the QSPTs and their critical points, however, during the past three years, a new approach has been proposed for the sake of shape coexistence phenomena and shape fluctuations phenomena [9][10][11][12].…”