The measurement of beta asymmetries at UNISOR/NOF using external plastic scintillator detectors

The performance of two external plastic scintillator detectors has been tested in an off-line mode using a source of¹⁰⁶RuFe at UNISOR/NOF. The measurement of beta asymmetries at various temperatures has resulted in the reproduction of the previously-determined magnetic dipole moment for the 1⁺ ground state of¹⁰⁶Rh and in addition the conclusion that the sign of this moment is positive.     

On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

Charge transfer states in GeO2-doped silicate fiber-optic waveguides and their role in second-harmonic generation

The concentration dependence of the broad-band luminescence arising in GeO₂-doped silicate fiber-optic waveguides is measured and interpreted. The spectra obtained show that electronic excitations of a new type that are absent in pure silicate glass — charge transfer excitons — arise in the doped system. Under the action of light an electron can be transferred both from a Ge center into the host and between Ge centers. Self-organization of these excitations in the field of a light wave (orientational ordering of their dipole moments) results in the appearance of a macroscopic electric field that destroys the initial centrosymmetry of the system and allows second-harmonic generation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 737–740 (25 November 1998)     

Paraelectric resonance of centers with icosahedral symmetry

The paraelectric resonance spectrum of non-central impurity ions situated in crystal fields of icosahedral symmetry is predicted. A multiwell potential is considered that corresponds to the displacement of the ions from the center of symmetry toward the vertices of the icosahedron, the faces of a dodecahedron, and the pentagonal faces of a fullerene molecule. The effective Hamiltonian of endohedral complexes in external electric fields with arbitrary orientation is obtained, its eigenvalues are found, and the line intensities of different transitions between the tunnelling levels are calculated. Fiz. Tverd. Tela (St. Petersburg) 39, 1693–1698 (September 1997)     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

Mutual coupling of elements in finite microstrip antennas

The mutual coupling of the radiating elements in microstrip antennas is studied using a rigorous electrodynamic approach in which the field singularities at the radiator edges are taken into account with analytic accuracy. A spectral method is employed in combination with a method of semi-inversion by extraction of the Green-function singularity. The degree of interaction of the elements of microstrip structures at the fundamental and higher current harmonicsis determined, and the applicability of various approximations is assessed.Radio-Astronomy Institute, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 8, pp. 688–701, August, 1992.     

Infrared ellipsometry study of the oxidation mechanisms of hydrogenated amorphous silicon

A detailed study of the oxidation of plasma deposited amorphous silicon (a-Si : H) using infrared phase modulated ellipsometry (IRPME) is presented. a-Si : H is found to be resistant against air oxidation confirming previous measurements. A 5–6 Å thick oxide layer at the surface of a-Si : H is observed after a few months of exposure to air. The extreme sensitivity of IRPME is emphasized. In particular Si-O-Si and (O_n)Si-H stretching vibrations are identified at the film surface at the submonolayer level. The oxidation mechanisms are discussed. The weak reactivity of a-Si : H with atmosphere is correlated with the presence of a hydrogen rich thin layer at the top surface.     

Kravchuk polynomials and group representations

Kravchuk polynomials of a discrete variable and different types of Kravchuk q-polynomials are determined. The importance of these polynomials for the theory of representations of Lie and Chevalley groups and the theory of symmetric and quantum groups is shown. The article presents a survey of the contemporary results in these areas.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 888–901, July, 1992.     

Research problem

This section appears from time to time. Contributions are invited, and should be submitted to R C. Thompson, Mathematics Department. University of California, Santa Barbara, CA93106-3080, USA.