Volume 46, Issue 11

Die explizite Form des nichtlokalen Operators [(mc) 2 - (hṼ) 2 ] 1/2 als integraloperator wird für m≧0 auf C x c (ℝ 3 ) berechnet. Das Eigenwertproblem wird für δ- artige Potentiale und für den Oszillator diskutiert On the Square-Root Klein-Gordon Equation as Schrödinger Equation for Spin 0 We give an explicit expression for the non-local operator [(m c) 2 - (hṼ) 2 ] 1/2 on C x c (ℝ 3 ) for m≧0 The eigenvalue problem is discussed for δ-like potentials and for the oscillator.

When quantizing the classical Hamiltonian H (q,p,t) = [m 2 c 4 + (c p - e A(t,q)) 2 ] 1/2 + e V(t, q), commutators of the form [f (a), g(b)], where [a,b] is not a c-number, have to be evaluated. The concept of continuously symmetrized products enables us to derive a number of statements, such as a continuity equation for the density operator δ{q(t)-x)=n(t, x), in a formally concise way. We can also show, then, that the dependence of the Hamiltonian on higher powers of the kinetic momentum destroys the relativistic invariance of the theory, even if we admit a more general coupling of the external potentials than above.

From the 29 Si NMR spectrum of [(t-BuO) 3 SiSAg] 4 with a partly resolved fine structure recorded at 9.4 T, the coupling constants |J( 29 Si, 109 Ag)| = (4.49 ±0.04) Hz and | J( 29 Si, 107 Ag)| = (3.90 + 0.03) Hz were derived. The 109 Ag spectra at 9.4 T and at 2.1 T are single lines without fine structure shifted to higher frequency by δ = (725.8 ± 1.5) ppm relative to the resonance of the Ag + ion in aqueous solution at infinite dilution. No hint of any {Ag, Ag}-coupling can be derived from these spectra and from a comparison of the FID- and steady-state-signal intensities, i.e. | J (Ag, Ag) | < 1 Hz. This result is in contrast to the assumption of an Ag-Ag bond to explain the spatial shift of the Ag atoms towards the centre of the alternating Ag4S4-eight-membered central ring of the molecule. For the first time silver relaxation was investigated in a molecule. T 1 ( 109 Ag) was determined at 9.4 T and at 2.1 T and at different temperatures to separate the contributions of different mechanisms: chemical shift anisotropy is the dominating one. T 1 =20.2 s at 2.1 T and at 301 K in this molecule is shorter by nearly two orders of magnitude than T 1 of the Ag + ion in aqueous solution

Amorphous Ni-Zr-alloys can be prepared by melt-spinning within a wide range of composition. Studies by X-ray diffraction yielded structure factors, pair correlation functions, total coordination numbers and atomic distances in dependence on the nickel concentration in the range of 25 up to 45 atomic percent. The change of the total coordination number and atomic distances turned out to be linear with the composition in this range. This is in good agreement with the linear composition dependence of the superconducting transition temperature, magnetic susceptibility, crystallization temperature, and electrical resistivity in the investigated range of composition.

Using neutron diffraction as well as the method of isotopic substitution the partial Bhatia-Thornton as well as the partial Faber-Ziman structure factors of amorphous Ni 25 Zr 75 were determined. A compound forming tendency was found. The atomic distances, partial coordination numbers, and the chemical short range order parameter are evaluated.

Thermal oxidation of silicon is described as a three-component thermodynamic local process involving silicon, silicon oxide, and oxygen molecules. A simplified system of model equations is used to demonstrate the evoluton of the Si-SiO 2 interface. For the one-dimensional case the equivalence with the model of Deal and Grove could be shown analytically. For that purpose effective interface coordinates have been introduced which establish the connection between the conventional concept of sharp interfaces and our "diffusive" interface, i.e., a transition region between pure silicon and pure silicon oxide.

The predictions of SO (3) Gravitation Theory are studied for a homogeneous, isotropic universe. Various types of oscillations are obtained for the pre-inflationary phase, where the geometry experiences violent fluctuations. These are ultimately terminating at either re-collaps or regular inflation.

The hyperfine structure of the 4-Oxo-TEMPO (2,2,6,6-tetramethyl-4-oxopiperidin-oxyl-l) free radical was investigated. Theoretical investigation includes four methyl groups protons close to the unpaired electron. Energy levels and transition probabilities were found by using second order and first order perturbation theory, respectively, and from these data theoretical spectra of the free radical were obtained. Diluted solutions in CH 3 -OH were prepared and the spectra were recorded with a double resonance spectrometer (1.53 mT) and Varian E-9X-band ESR spectrometer ( ~ 0.3 T). In order to understand the influence of time dependent phenomena on the linewidths, electronic relaxation times of 4-Oxo-TEMPO and its perdeuterated form (PDT) were measured at two different fields by using cw saturation method.

The temperature dependence of the dynamic dipole polarizability α(λ) of gaseous neopentane has been re-examined in the temperature range between T = 250 K and T - 360 K at the four HeNelaser wavelengths λ = 543.51 nm, 594.11 nm, 611.97 nm, and 632.99 nm. These interferometric measurements are compared with former determinations of the dynamic as well as the static dipole polarizability in the solid, liquid and gaseous state. In all cases, a shape of α(T) in the range between 290 K and 310 K has been observed which is similar to the shape of α (λ) in an absorption band. This observation is connected with other physico-chemical quantities of neopentane.

Nuclear quadrupole hyperfine structures have been resolved in the rotational spectrum of thionyl aniline, C 6 H 5 NSO, using pulsed molecular beam microwave Fourier transform spectroscopy. High precision nuclear quadrupole coupling constants, rotational and quartic centrifugal distortion constants have been determined from the analysis of 12 low-J transitions. Coupling constants are χ aa = + 1.5730(14) MHz and (χ bb - χ cc )= -5.6499(13) MHz. rotational constants are A-4026.72i5(4) MHz, B = 860.64732(8) MHz, and C = 709.52027(7) MHz, and centrifugal distortion constants are Δ J - 36.6(5) Hz, Δ JK = -107.5(20) Hz, Δ K = 703(68) Hz, δ J = 8.1(5) Hz, and δ K =111(19) Hz (representation I' used).

The radical species derived from cyclopentane, cyclopentenes and cyclohexenes by 60 Co γ-ray irradiation at 77 K in halocarbon matrices have been studied by ESR spectroscopy. The electronic and geometrical structures of the radical species are discussed on the basis of the experimental hyperfine coupling constants and semiempirical MO calculations. Exposure of the tetramethylsilane frozen solution containing cyclopentene to 60 Co γ-rays produced specifically 3-cyclopenten-l-yl.

The dielectric spectrum is measured up to 72 GHz of solutions of polyvinylpyrrolidone (PVP) in tetramethylurea (TMU), dimethylethylene urea and dimethylpropylene urea. Concentrations are up to a monomole fraction of 0.65 (PVP 1200) or 0.5 (PVP 40 000). Measuring temperatures are 20CC for all systems and additionally 40 and 60°C for the TMU solutions. For the description of the results a superposition of Debye type components is used, which are discussed in particular with respect to the solvent contributions. These can be distinguished into three regions: (i) Unaffected bulk-type; (ii) loosely affected, relaxation time and activation enthalpy increasing with increasing polymer content; (iii) quasi bound and moving together with the polymer. The solvation numbers (total of affected solvent per repeat unit of polymer) are about 1.5 to 2.