Numerical convergence study of the orthogonalized multi-channels approach to three-body Coulomb scattering below breakup threshold

The three-body Coulomb problem for nuclear clusters is solved numerically for a model below three-body breakup threshold. An orthogonalized multi-channels method is employed. The method allows to check for convergence by considering the norm square of the closed-channels part of the wave function. The numerical results show that convergence can well be achieved on present-day computers.     

Wellposedness for the Navier–Stokes flow in the exterior of a rotating obstacle

In this paper we study the Navier–Stokes boundary‐initial value problem in the exterior of a rotating obstacle, in two and three spatial dimensions. We prove the local in time existence and uniqueness of strong solutions. Moreover, we show that the solutions are global in time, in two spatial dimensions. Copyright © 2005 John Wiley & Sons, Ltd.     

Delayed self-heterodyne linewidth measurement of VCSELs

We report on high-resolution linewidth measurements of proton-implanted InGaAs-GaAs VCSELs employing the delayed self-heterodyne method. Devices with 16-/spl mu/m active diameter exhibit record low linewidths of 20 MHz and 4-MHz residual linewidth. The linewidth enhancement factor is accurately determined from the ratio of induced phase to amplitude modulation indexes.     

Off-shell behaviour of theN-N interaction in a six-quark resonating group model of the deuteron

Two different 6-quark resonating group models of the deuteron are investigated to study the off-shell property of theN-N interaction. In the first model the quarks interact by a central one-gluon-exchange potential plus confinement potential. The meson-exchange contribution to then-p potential is simulated by a central GaussianN-N potential. In the second model the quarks interact by one-gluon-and one-pion-exchange potentials (central and noncentral) plus confinement potential. A small additional -exchange potential between neutron and proton binds the deuteron at the correct energy.Several off-shell variants of the two resonating group models are compared with each other by analyzing their elastic electron scattering cross sections. It is found that the standard renormalized version of the resonating group model yields potentials and wave functions that may be considered physical within the limitations of the model. Unitary off-shell transformations, which modify potentials and wave functions in any sizeable way, lead to a disagreement between the charge distribution predicted by the model via analysis of electron scattering and the charge distribution following from the microscopic quark distribution.Both of the 6-quark models support a soft repulsive core of the tripletn-p potential with a core height of around 900 MeV.     

Kinetik und stereochemischer Verlauf der thermischen Umlagerung der vier stereoisomeren Propenyl-(but-2′-enyl)-äther

The gas-phase rearrangement of (1Z, 2′E)-, (1Z, 2′Z)-, (1E, 2′E)-, and (1E, 2′Z)- propenyl but-2′-enyl ether (Z, E)-, (Z, Z)-, (E, E)-, and (E, Z)-1) into erythro- and threo-2, 3-dimethyl-pent-4-en-al (erythro- and threo-2) was investigated over a temperature range from 142,5° to 190,0° at 20–35 Torr (for kinetic data and activation parameters see table 2). All four stereoisomeric ethers 1 rearrange preferentially via a chair-like transition state C into the aldehydes 2 (ΔΔG^≠ (160°) = 2,5–2,7 kcal/mol for B – C (B = boat-like transition state). The relative rates (k_rel) for (Z, Z)-1, (Z, E)-1, (E,Z)-1, and (E,E)-1 at 160° are 1,0, 2,9, 4,3 and 9,0 respectively (see table 5). Taking into account the relative enthalpies of the ethers 1 and the steric interaction in the C transition state of the ethers 1 (see table 6), k_rel values can be estimated. They are in good agreement with those observed (see table 5).     

Ferromagnetic coupling through spin polarization in the hexanuclear [MnII(3)CuII(3)] complex

A novel Cu(II)-Mn(II) hexanuclear complex of formula [[MnCuL](3)(tma)](ClO(4))(3).8H(2)O [H(2)L = macrocyclic Robson proligand; H(3)tma = trimesic acid] has been obtained by connecting three heterobinuclear [Cu(II)Mn(II)L](2+) cationic species through the trimesate anion. The complex exhibits a C(3) rotational symmetry, imposed by the geometry of the bridging ligand. The interaction within each Mn(II)-Cu(II) pair is antiferromagnetic (J = -16.7 cm(-1)). A weak ferromagnetic coupling among the three S = 2 resulting spins through the tricarboxylato bridge leads to a S = 6 ground spin state, for which the spin polarization mechanism is responsible.     

High-temperature synthesis, single-crystal X-ray structure determination and solid-state NMR investigations of Ba7[SiO4][BO3]3CN and Sr7[SiO4][BO3]3CN

The novel alkaline earth silicate borate cyanides Ba₇[SiO₄][BO₃]₃CN and Sr₇[SiO₄][BO₃]₃CN have been obtained by the reaction of the respective alkaline earth metals M=Sr, Ba, the carbonates M^IICO₃, BN, and SiO₂ using a radiofrequency furnace at a maximum reaction temperature of 1350°C and 1450°C, respectively. The crystal structures of the isotypic compounds M^II₇[SiO₄][BO₃]₃CN have been determined by single-crystal X-ray crystallography (P6₃mc (no. 186), Z=2, a=1129.9(1) pm, c=733.4(2) pm, R₁=0.0336, wR₂=0.0743 for M^II=Ba and a=1081.3(1) pm, c=695.2(1) pm, R₁=0.0457, wR₂=0.0838 for M^II=Sr). Both ionic compounds represent a new structure type, and they are the first examples of silicate borate cyanides. The cyanide ions are disordered and they are surrounded by Ba²⁺/Sr²⁺ octahedra, respectively. These octahedra share common faces building chains along [001]. The [BO₃]³⁻ ions are arranged around these chains. The [SiO₄]⁴⁻ units are surrounded by Ba²⁺/Sr²⁺ tetrahedra, respectively. The title compounds additionally have been investigated by ¹¹B, ¹³C, ²⁹Si, and ¹H MAS-NMR as well as IR and Raman spectroscopy confirming the presence of [SiO₄]⁴⁻, [BO₃]³⁻, and CN⁻ ions.