Evidence for Triangular D_{3h}^{'} Symmetry in ^{13}C.

We derive the rotation-vibration spectrum of a 3α+1 neutron(proton) configuration with triangular D_{3h} symmetry by exploiting the properties of the double group D_{3h}^{'} and show evidence for this symmetry to occur in the rotation-vibration spectra of ^{13}C. Our results, based on purely symmetry considerations, provide benchmarks for microscopic calculations of the cluster structure of light nuclei.

Origin of low-lying enhanced E1 strength in rare-Earth nuclei.

The experimental E1 strength distribution below 4 MeV in rare-earth nuclei suggests a local breaking of isospin symmetry. In addition to the octupole states, additional J^{π}=1^{-} states with enhanced E1 strength have been observed in rare-earth nuclei by means of (γ,γ') experiments. By reproducing the experimental results, the spdf interacting boson model calculations provide further evidence for the formation of an α cluster in medium-mass nuclei and might provide a new understanding of the origin of low-lying E1 strength.

Evidence for tetrahedral symmetry in (16)O.

We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band.

A study of the bending motion in tetratomic molecules by the algebraic operator expansion method.

We study the bending motion in the tetratomic molecules C2H2 (X̃ (1)Σg (+)), C2H2 (Ã (1)Au) trans-S1, C2H2 (Ã (1)A2) cis-S1, and X̃ (1)A1 H2CO. We show that the algebraic operator expansion method with only linear terms comprised of the basic operators is able to describe the main features of the level energies in these molecules in terms of two (linear) or three (trans-bent, cis-bent, and branched) parameters. By including quadratic terms, the rms deviation in comparison with experiment goes down to typically ∼10 cm(-1) over the entire range of energy 0-6000 cm(-1).

Limits on neutrino masses from neutrinoless double-β decay.

Neutrinoless double-β decay is of fundamental importance for the determining neutrino mass. By combining a calculation of nuclear matrix elements within the framework of the microscopic interacting boson model with an improved calculation of phase space factors, we set limits on the average light neutrino mass and on the average inverse heavy neutrino mass (flavor-violating parameter).

A novel algebraic scheme for describing coupled benders in tetratomic molecules.

An algebraic scheme for describing the bending dynamics of tetratomic molecules including linear, bent planar, and bent a-planar species is introduced. The correlation diagram linear-cis-bent and linear-trans-bent is constructed. Effective potential energy functions are evaluated by exploiting the method of coherent states.

Dynamic supersymmetries of differential equations with applications to nuclear spectroscopy.

Dynamic supersymmetries of differential equations are defined. The case of a liquid drop with quadrupole deformation coupled to a particle with j = 3/2 is shown as an example of a situation where the dynamic supersymmetry OSp(5/4) may occur. A special solution, called E(5/4), of interest in the spectroscopy of odd-even nuclei in the transitional region between spherical and gamma unstable is explicitly worked out.

Phase structure of the two-fluid proton-neutron system.

The phase structure of a two-fluid bosonic system is investigated. The proton-neutron interacting boson model possesses a rich phase structure involving three control parameters and multiple order parameters. The surfaces of quantum phase transition between spherical, axially symmetric deformed, and SU(*)(pinu)(3) triaxial phases are determined.

Quantum phase transitions in mesoscopic systems.

Quantum phase transitions in mesoscopic systems are studied. It is shown that the main features of phase transitions, defined for infinite number of particles, N--> infinity, persist even for moderate N approximately 10. A Landau analysis of first order transitions is done and a "critical" exponent at the spinodal point is defined.

Phase transitions in angle variables.

Phase transitions in angle variables are studied. An example of angular phase transition, an axially to triaxially deformed "shape" transition in nuclei, is discussed. Spectroscopic signatures for the occurrence of these transitions are suggested.

Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition.

An approximate solution at the critical point of the spherical to axially deformed shape phase transition in nuclei is presented. The eigenvalues of the Hamiltonian are expressed in terms of zeroes of Bessel functions of irrational order.

Dynamic symmetries at the critical point.

A new class of dynamic symmetries is introduced. It is suggested that an element of this class, associated with zeros of Bessel functions, be used to describe spectra of nuclei at or around the critical point of the U(5)-SO(6) shape phase transition, and, in general, spectra of systems undergoing a (second order) phase transition between the algebraic structures U(n-1) and SO(n).