A. Leviatan

Algebraic Treatment of Collective Excitations in Baryon Spectroscopy

Algebraic methods have been used extensively in hadronic physics for the description of the internal degrees of freedom (flavor-spin-color) [1]. Spectrum generating algebras and dynamic symmetries have been very instrumental in the classification of hadronic states and the construction of mass formulas, such as the Gell-Mann-Okubo mass formula [2].

Deformed pseudospin doublets as a fingerprint of a relativistic supersymmetry in nuclei

The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the relativistic pseudospin symmetry of the nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.

Partial dynamical symmetries in quantum systems

We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of Hamiltonians with this property, including higher-order terms, and portray their significance for spectroscopy and shape-phase transitions in nuclei. The occurrence of both a single PDS, relevant to stable structures, and of several PDSs, relevant to coexistence phenomena, are considered.

Exact dynamical and partial symmetries

We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.

Symmetries at and Near Critical Points of Quantum Phase Transitions in Nuclei

We examine several types of symmetries which are relevant to quantum phase transitions in nuclei. These include: critical‐point, quasidynamical, and partial dynamical symmetries.

Partial Dynamical Symmetry and Anharmonicity in Gamma‐Soft Nuclei

Partial dynamical symmetry is shown to be relevant for describing the anharmonicity of excited bands in 196Pt while retaining solvability and good SO(6) symmetry for the ground band.

Supersymmetric structure in the Dirac equation with cylindrically‐deformed potentials

Classes of relativistic symmetries accommodating supersymmetric patterns are considered for the Dirac Hamiltonian with axially‐deformed scalar and vector potentials.

Critical‐Point Structure in Finite Nuclei

Properties of quantum shape‐phase transitions in finite nuclei are considered in the framework of the interacting boson model. Special emphasis is paid to the dynamics at the critical‐point of a general first‐order phase transition.

RELATIVISTIC PSEUDOSPIN SYMMETRY AS A SUPERSYMMETRIC PATTERN IN NUCLEI

Shell-model states involving several pseudospin doublets and ``intruder levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.

Relativistic Pseudospin Symmetry and the Structure of Nuclear States

The concept of pseudospin symmetry [1, 2] is based on the empirical observation of quasi-degenerate pairs of certain normal-parity shell-model orbitals with non-relativistic quantum numbers n n