Symmetries and supersymmetries of the dirac hamiltonian with axially deformed scalar and vector potentials.

We consider several classes of symmetries of the Dirac Hamiltonian in 3 + 1 dimensions, with axially deformed scalar and vector potentials. The symmetries include the known pseudospin and spin limits and additional symmetries which occur when the potentials depend on different variables. Supersymmetries are observed within each class and the corresponding charges are identified.

Partial dynamical symmetry in quantum Hamiltonians with higher-order terms.

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have selected classes of solvable states. The method is illustrated in the SO(6) limit of the interacting boson model of atomic nuclei and applied to the nucleus 196Pt.

Partial dynamical symmetry at critical points of quantum phase transitions.

We show that partial dynamical symmetries can occur at critical points of quantum phase transitions, in which case underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several types of partial dynamical symmetries are demonstrated with the example of critical-point Hamiltonians for first- and second-order transitions in the framework of the interacting boson model, whose dynamical symmetries correspond to different shape phases in nuclei.

Supersymmetric patterns in the pseudospin, spin, and coulomb limits of the dirac equation with scalar and vector potentials.

We show that the Dirac equation in (3+1) dimensions gives rise to supersymmetric patterns when the scalar and vector potentials are (i). Coulombic with arbitrary strengths or (ii). when their sum or difference is a constant, leading to relativistic pseudospin and spin symmetries. The conserved quantities and the common intertwining relation responsible for such patterns are discussed.

Critical-point symmetry in a finite system.

At a critical point of a second-order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can describe the dynamics at the critical point. This effective deformation is determined by minimizing the energy surface after projection onto the appropriate symmetries. We derive analytic expressions for energies and quadrupole rates which provide good estimates for these observables at the critical point.

Generalized partial dynamical symmetry in nuclei.

We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.

Test of nuclear wave functions for pseudospin symmetry.

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.

Partial dynamical symmetry in a fermion system

The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell model of nuclei and shown to be closely related to the quadrupole-quadrupole interaction. Implications are discussed for the deformed light nucleus 20Ne.

[Epidemiology of Hansen's disease in Israel].

There are currently 200 patients with Hansen's disease in Israel who are being followed by the Hansen's Disease Government Hospital and the Ministry of Health (prevalence 4.4/100,000). Most of them immigrated from countries where the disease is endemic. Dermatological findings dominated the initial clinical picture, although 5% of patients are asymptomatic contacts of known cases. Age at onset of disease was less than 20 years in 1/4 of the cases. The incidence in Israel is falling: 0.4/100,000 in 1985-89 compared to 3.6/100,000 in 1950-54. Neurologic and dermatologic findings in an immigrant of any age originating from countries where Hansen's disease is endemic, should prompt appropriate diagnostic evaluation, even years after immigration to Israel. Contacts of known cases of Hansen's disease should be aggressively screened, even if asymptomatic.