Magnetic moments of hindered rotators by off‐center impurity ions

Off‐center impurity ions in solids often perform rotations around their regular lattice sites. Unlike quasifree rotors with rotational line spectra subject to textbook attention in quantum mechanics, the off‐center species are hindered rotors with spectra quantized in rotational bands. These bands occur because of tunneling through barriers arising along the orbital path. For an off‐center ion rotating along a planar orbit, such as the Li⁺ impurity nearest‐neighboring an F center in alkali halide, the hindered rotation will give rise to specific magnetic moments that couple to and quantize external magnetic fields normal to the orbital plane. We present a simple theory and estimates of Li⁺ magnetic dipoles and rotational bands to find conditions for an experimental verification. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Piezoelectricity of ordered (ScxGa1-xN) alloys from first principles

First-principles calculations are performed to compute the e₃₃ piezoelectric coefficients of GaN, ScN and (Sc_xGa_1-xN) alloys exhibiting an alternation of hexagonal GaN, with hexagonal ScN along the c-axis. For Sc compositions larger than 50%, each atom has nearly five nearest neighbors (i.e., the ground state exhibits a phase that is five-fold coordinated). On the other hand, Sc-deficient (Sc, Ga) N alloys adopt a ground-state that is four-fold coordinated). The magnitude of e₃₃ in the Sc-deficient ideally ordered (Sc_0.25Ga_0.75N) is found to be larger than the magnitude of the corresponding e₃₃ coefficients resulting from the compositional weighted average over the hexagonal (h-ScN) and the wurtzite (w-GaN) parent compounds. On the other hand, the e₃₃ coefficients of the Sc-rich ordered (Sc_0.75Ga_0.25N) is found to be negligibly small. In addition, e₃₃ piezoelectric coefficients in ordered (Sc_0.5Ga_0.5N) exhibit quite large magnitudes, due to the nonpolar to polar transition occurs at Sc composition x = 0.5, and thus can bridge the corresponding coefficients of (Ga, In) N and ferroelectric alloys. The microscopic origins for this huge enhancement in the piezoelectric behavior in Sc-low and Sc-intermediate alloys and the role of each atom are revealed and discussed.     

The nucleon wave function at the origin

We calculate the next-to-leading order perturbative corrections to the SVZ sum rules for the coupling fN$f_N$, the nucleon leading twist wave function at the origin. The results are compared to the established Ioffe sum rules and also to lattice QCD simulations.     

Configuration interactions constrained by energy density functionals

A new method for constructing a Hamiltonian for configuration interaction calculations with constraints to energies of spherical configurations obtained with energy-density-functional (EDF) methods is presented. This results in a unified model that reproduced the EDF binding-energy in the limit of single-Slater determinants, but can also be used for obtaining energy spectra and correlation energies with renormalized nucleon–nucleon interactions. The three-body and/or density-dependent terms that are necessary for good nuclear saturation properties are contained in the EDF. Applications to binding-energies and spectra of nuclei in the region above ²⁰⁸Pb are given.     

Die Korrektur des Bildes der Anger-Kamera (Teil II)

Ausgehend von der im ersten Teil begründeten Notwendigkeit, die mit der Szintillationskamera Impulsverteilung korrigieren zu müssen, wird in der vorliegenden Arbeit der Programmablanfplan für diese Korrekturrechnung mit Hilfe der elektronischen Datenverarbeitung (R 300) erläutert. Im gegenwärtigen Stadium der Entwicklung eines umfangreichen Konzepts zum Einsatz der EDV für die Szintigraphie – an der alle Nuklearmedizinischen Abteilungen der DDR beteiligt sind – erfolgt bei den Autoren die Ein- und ausgabe der Daten über Lochstreifen. Die Wirkung der Korrekturrechnung wird am homogenen Phantom selbst und an einer Pankreasunfersuchung demonstriert.     

Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique

A nested non-linear multigrid algorithm is developed to solve the Navier–Stokes equations which describe the steady incompressible flow past a sphere. The vorticity–streamfunction formulation of the Navier–Stokes equations is chosen. The continuous operators are discretized by an upwind finite difference scheme. Several algorithms are tested as smoothing steps. The multigrid method itself provides only a first-order-accurate solution. To obtain at least second-order accuracy, a defect correction iteration is used as outer iteration. Results are reported for Re = 50, 100, 400 and 1000.     

A note on grating based soft X-ray monochromators

A few facts related to the aberrations for toroidal and plane gratings are presented. Some design aspects of the plane grating-based monochromator devised by Petersen (1982) are discussed. We also point out that for a cylindrical grating astigmatic correction can be reduced and suggest that following Petersen’s scheme some improvements in the monochromator performance could be achieved with such a grating.     

Analysis and optimisation of the tuning of the twelfths for a clarinet resonator

Even if the tuning between the first and second register of a clarinet has been optimized by instrument makers, the lowest twelfths remain slightly too large (inharmonicity). In this article, we study the problem from two different points of view. First, we systematically review various physical reasons why this inharmonicity may take place, and the effect of different bore perturbations inserted in cylindrical instruments such as bore flare, open and closed holes, taper, temperature gradients, visco-thermal effects, etc. Applications to a real clarinet resonator and comparisons with impedance measurements are then presented. A commonly accepted idea is that the register hole is the dominant cause for this inharmonicity: it is natural to expect that opening this hole will shift the position of the resonances of the instrument to higher frequencies, except of course for the note for which the hole is exactly at the pressure node. We show that the real situation is actually more complicated because other effects, such as open holes or bore taper and bell, introduce resonance shifts that are comparable but with opposite sign, so that a relatively good overall compensation takes place. This is checked by experimental and theoretical studies of the acoustical impedance curves of a clarinet. The origin of the observed inharmonicity in playing frequencies is therefore different, maybe related to the reed or the vocal tract. In a second part, we use an elementary model of the clarinet in order to isolate the effect of the register hole: a perfect cylindrical tube without closed holes. Optimization techniques are then used to calculate an optimum location for the register hole (without taking into account the use of the register hole as a B flat tone hole); the result turns out to be close to the location chosen by clarinet makers. Finally, attempts are made numerically to improve the situation by introducing small perturbations in the higher part of the cylindrical resonator, but no satisfactory improvement is obtained.