Bestimmung des Abschirmtensors der magnetischen Kernresonanz und des Tensors der magnetischen Suszeptibilität durch numerische Berechnung der Stromdichte in der Ladungsverteilung diamagnetischer Moleküle

Determination of the NMR Shielding Tensor and of the Tensor of Magnetic Susceptibility by Numerical Calculation of the Current Density in the Chargedistribution of Diamagnetic Molecules In papers [1] and [2] a semiclassical approach for calculation of the NMR shielding tensor and of the tensor of magnetic susceptibility of diamagnetic molecules was represented by SCHMIEDEL. In this method the equation of continuity for the currents in the electronic cloud induced by an external magnetic field must be solved. In this paper a method of numerical solution of this partial differential equation is developed. The H₂-molecule serves as an example to present the possibilities of this method.     

Bestimmung der Abschirmung der magnetischen Kernresonanz und der magnetischen Suszeptibilität durch Berechnung der Stromdichte diamagnetischer Moleküle mit der Methode der finiten Elemente

Determination of the NMR-Shielding and of Magnetic Susceptibility by Calculation of the Current Density of Diamagnetic Molecules by the Finite Element Method In paper [20] the finite element method was initiated for calculations of diamagnetic properties of molecules on the basis of a semiclassical approach [18, 19]. In the present work this method is used in the frame of the uncoupled Hartree-Fock-perturbation theory. It is shown that the proposed approach is applicable to localized orbitals, the susceptibility and the shielding being divided into incrementary contributions. Furthermore the relationship to the semiclassical approach and to the approach of Rebane [7] is shown. The H₂-molecule, the threedimensional anisotropic harmonic oscillator and the CH₄-molecule serve as examples to present the possibilities of this method.     

Zur Deutung der magnetischen Streifenverschiebung in Elektronen-Interferometern

Attempts to explain the magnetic fringe shift in electron interferometers by means of classical force concepts are shown to be wrong, because the basic assumption that the magnetic field of an electron moving outside a coil can penetrate the turns without any perturbation is shown to be invalid. One simple example for strong shielding of the external field is given.     

Paketimpulse in der magnetischen Kernresonanz

Composite Pulses in Nuclear Magnetic Resonance For the compensation of spatial inhomogeneity of the radiofrequency field and a resonance offset in NMR experiments, composite pulses are used instead of the conventional single pulses. In the present work the effect of a resonance offset on composite pulses is treated quantitatively. It will be shown also experimentally that the various constructions for \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{\pi }{2} $\end{document} composite pulses (contrary to π composite pulses) lead to only two different degrees of compensation depending on the choice of the phase of the pulses or the sign of the resonance offset.     

Density matrix in technique of polarized ion sources

The use of the density matrix is the most direct way to work with polarization parameters. The solutions of the equation for the density matrix are obtained for hydrogen and deuterium. The magnetic moments of nuclei are explicitly incorporated into the equations, even though numerically it does not make a big difference. It is shown that in the general case the density matrix can not be reduced to the one with the only spin variables of the nucleus in contradiction with the statement of K. Blum [K. Blum, Density Matrix Theory and Applications].     

Der Interferenzeffekt in der magnetischen Kernrelaxation für Vierspin-Systeme. V

The interference of intramolecular dipole-dipole interaction and anisotropy of electronic screening in nuclear magnetic relaxation is taken into account for systems containing four identical nuclei of spin 1/2 located at the corners of a tetrahedral, a square and a rectangle. The influence of spinrotational interaction is also considered. The results, presented in the paper show that, due to the interference effect, a significant deviation of a pure exponential time dependence of nuclear magnetization in some special cases may appear.     

Ein vollständig automatisiertes Meßverfahren zur Bestimmung der magnetischen Nachwirkung in ferromagnetischen Kristallen

Temporal changes of the initial susceptibility of ferromagnetic crystals can be measured advantageously via the resonance frequency of an LC-oscillator. Due to its decreasing susceptibility during the magnetic desaccomodation, the crystal under investigation — which is taken as the core of the oscillatory circuit — induces definite changes of the resonance frequency. The essential advantage of this measuring method consists of the digital acquisition of the measured data, which may form the basis of a complete automation of the desaccomodation experiment. This work describes a device, in which all possibilities of automation — offered by this new measuring method — are realized in a consequent manner.     

Stochastische theorie der magnetischen relaxation. II

A stochastic theory of magnetic relaxation developped in a former work is expanded. As an application the longitudinal nuclear spin-spin-relaxation in solids and spinlattice-relaxation in liquids are treated. Oscillating relaxation functions are calculated. The results are in good agreement with experimental measurements at CaF₂.     

Stochastische Theorie der magnetischen Relaxation

Let a single magnetic dipole be in a constant magnetic field ?₀ and a fluctuating field ?′(t). For this problem the equation of motion is solved exactly. Averaging the magnetic moment over a convenient ensemble relations of relaxation of a macroscopic system of many spins are obtained. In this way a relaxation tensorΦ for magnetisation is derived from the stochastic properties of the fluctuating field which is a generalization ofKubo's oscillator model. For small timesΦ approaches a Gaußian for large times an exponential function. There are two relaxation times which may be expressed by two correlation times of the fluctuating field. The results give a classification of the absorption line shape in Gaußian and Lorentzian type.     

Untersuchungen zur Struktur des Triglycinsulfats mit Hilfe der hochauflösenden magnetischen Kernresonanzspektroskopie im Festkörper

Investigations of the Structure of Triglycinsulfate by High Resolution Magnetic Resonance in Solids Measurements were performed in the ferroelectric and paraelectric phase of TGS monocrystals with the aid of multiple pulse experiments for high resolution magnetic proton resonance in solids. The contributions to the spectra, which are to be expected theoretically from the different proton groups (NH₃, CH₂, OH), were calculated and compared with the corresponding experimental results. Splittings are discussed, which occur as a consequence of the ¹⁴N? ¹H-interaction and indicate changes at the phase transition point. The anisotropy of the effective chemical shift tensor caused by the rotation of NH₃-groups and the anisotropy of the chemical shift tensor of OH-groups were determined.     

Splitting based finite volume schemes for ideal MHD equations

We design finite volume schemes for the equations of ideal magnetohydrodynamics (MHD) and based on splitting these equations into a fluid part and a magnetic induction part. The fluid part leads to an extended Euler system with magnetic forces as source terms. This set of equations are approximated by suitable two- and three-wave HLL solvers. The magnetic part is modeled by the magnetic induction equations which are approximated using stable upwind schemes devised in a recent paper [F. Fuchs, K.H. Karlsen, S. Mishra, N.H. Risebro, Stable upwind schemes for the Magnetic Induction equation. Math. Model. Num. Anal., Available on conservation laws preprint server, submitted for publication, URL: <http://www.math.ntnu.no/conservation/2007/029.html>]. These two sets of schemes can be combined either component by component, or by using an operator splitting procedure to obtain a finite volume scheme for the MHD equations. The resulting schemes are simple to design and implement. These schemes are compared with existing HLL type and Roe type schemes for MHD equations in a series of numerical experiments. These tests reveal that the proposed schemes are robust and have a greater numerical resolution than HLL type solvers, particularly in several space dimensions. In fact, the numerical resolution is comparable to that of the Roe scheme on most test problems with the computational cost being at the level of a HLL type solver. Furthermore, the schemes are remarkably stable even at very fine mesh resolutions and handle the divergence constraint efficiently with low divergence errors.     

Calculation of spin resonance strength at COSY accelerator

The influence of RF dipole on spin motion at the COSY accelerator was studied in [1, 2]. The discrepancy between the theoretically calculated spin resonance strength for the deuteron beam and the experimentally observed value were discovered [2]. In this work it is shown that the calculation using the response function makes explaining the discrepancy between experimental data and theoretical calculations of spin resonance strengths induced by modulated radial magnetic dipole possible.     

Einfluß einer Quasiteilchen-Spinbahnwechselwirkung auf die magnetischen Momente leichter Atomkerne

Using Migdal's theory of interacting quasiparticles, the influence of a two-body spin-orbit interaction in addition to the spin-spin interaction on magnetic moments of nuclei was investigated in the mass regionA=11 toA=65. The coupling constants of the spin-orbit interaction were determined from spin-orbit splittings of single particle energies, and those of the spin-spin interaction were adjusted by fitting magnetic moments. The constants of the spin-spin interaction were found to be dependent on the mass value. The inclusion of the spin-orbit interaction led to a better agreement of theoretical and experimental magnetic moments of light nuclei. The spin-orbit contribution was averaged 7% over all nuclei, but reached 20–30% for some of them.     

Magnetic shielding tensors of carbon nuclei in 3,5-dichlorophenylacetylene,a theoretical ab initio and experimental study

Ab initio GIAO-CHF and DFT(B3LYP) molecular geometry optimization and magnetic shielding tensor calculations of carbon nuclei of 3,5-dichlorophenylacetylene have been performed using 6–311G?? and 6–311+G(2d,p) basis sets. The isotropic ¹³C chemical shifts, needed for comparison, have been measured in C₆D₁₂ solution. The principal elements of the shielding tensor of the carbon nuclei in the investigated molecule in the solid state have been determined from an intensity analysis of the spinning sidebands in ¹H-¹³C CP/MAS NMR spectra. Shielding anisotropy parameters of the acetylenic carbons have been independently determined using the method based on proton-coupled ¹³C nematic phase spectra as well as from the interpretation of the ¹³C longitudinal relaxation rates. The latter data have been analysed assuming the molecular reorientation to be the rotational diffusion of an asymmetrical top, which has provided, apart from the diffusion coefficients, an additional check on the reliability of the theoretical calculation of the shielding tensors. In general, satisfactory agreement between the theoretical and experimental results has been achieved.     

Intramolecular dynamics in small radicals with anisotropic magnetic interactions

The ESR lineshape of one electron spin coupled by anisotropic hyperfine interaction to two nuclei is calculated when two different configurations of the molecule interchange by a simple reaction scheme. The spectrum calculation includes the anisotropic electron Zeeman interaction and the nonsecular terms of the electron spin. The lineshape, which simulates both a nonsaturated CW or a pulse experiment, is calculated numerically by using a density matrix theory within the Liouville formalism. The theory is tested against the X-band spectra of-CH₂ in ZnAc single crystal for three different orientations of the magnetic field. The present theoretical lineshape reproduces all the experimental “forbidden” transitions and predicts that they are important for certain crystal orientations. The calculated reorientation barrier of the methylene in the present work is 7.17 kcal/mol which is closer to an estimated minimum value of 9 kcal/mol, than the previous value of 5–6 kcal/mol obtained by an analysis with the modified Bloch equations.     

Elektronen-Interferenzen in der Umgebung der Brennlinie einer magnetischen Quadrupollinse

It is shown that a coherent superposition of parts of an electron wave field by magnetic fields is possible. The deflecting magnetic fields are formed by a quadrupole lens. The interference space in which the coherent superposition of three partial waves takes place is limited by a caustic surface. The interference phenomena in the neighbourhood of this surface can be described by means of an integral of the Airy type. A quadrupole lens with rectangular pole piece edges forms in great distance from its axis homogeneous magnetic fields of opposite direction. If a coherent irradiation of both these homogeneous fields can be achieved, they form a magnetic biprism if the paraxial part of the beam is stopped. The distance of interference fringes in such an interferogram would in first approximation be independent of the particle energy.     

Zur Quantentheorie der magnetischen Widerstandsänderung

Considering a system of free electrons and randomly fixed impurities in a homogenious magnetic field, a derivation of a Titeica-type-formula for the transvers electrical conductivity is given. This formula holds for all magnetic field strengths and powers of the density of impurities. The derivation avoids an ergodic hypothesis for bounded variables which is used byKubo and coworkers. Also, a transport equation is derived, correct to the first power of the impurity density, from which the conductivity parallel to the magnetic field may be calculated. In both cases singularities which arise in the Born approximation are removed byt-matrix approximations.     

Screening corrections in cold deuterium fusion rates

We have recalculated the fusion rates of the free deuterium molecule, ion and mesomolecule taking into account the shielding of the Coulomb barrier by the electrons and muon. Electron screening increases the rates by several orders of magnitude. The fusion of hydrogen nuclei is known to be the source of energy of stars occuring in their high-temperature, high-pressure interiors. In terrestrial conditions, one attempts currently to tap this source of nuclear fusion energy by alternative techniques, i.e. high-temperature plasmas or muon-catalyzed fusion. Very recently cold fusion in solids has achieved worldwide attention, since experimental evidence for increased hydrogenic fusion rates in palladium and titanium has been reported[1,2]. These reports have motivated us to reconsider the fusion probability of free hydrogen molecules, ions and mesomolecules, following closely the studies of Refs. [3,4,5]. Our aim however is to improve the previous estimates of the respective fusion rates by taking account of the screening effects of the electrons and muons on the nuclear Coulomb barrier which will turn out to be quite important. As in Ref. [5] we will restrict our numerical results to deuterium only.     

Susceptibility corrections in solid-state NMR experiments with oriented membrane samples. Part I: applications

Chemical shift referencing of solid-state NMR experiments on oriented membranes has to compensate for bulk magnetic susceptibility effects that are associated with the non-spherical sample shape, as described in the accompanying paper [J. Magn. Reson. 164 (2003) 115-127]. The resulting frequency deviations can be on the order of 10 ppm, which is serious for nuclei with a narrow chemical shift anisotropy such as 1H or 13C, and in some cases even 19F. Two referencing schemes are proposed here to compensate for these effects: A flat (0.4 mm) glass container with an isotropic reference molecule dissolved in a thin film of liquid is stacked on top of the oriented membrane sample. Alternatively, the intrinsic proton signal of the hydrated lipid can be used for chemical shift referencing. Further aspects related to magnetic susceptibility are discussed, such as air gaps in susceptibility-matched probeheads, the benefits of shimming, and limitations in the accuracy of orientational constraints. A biological application is illustrated by a series of experiments on the antimicrobial peptide PGLa, aimed at understanding its concentration-dependent membranolytic effect. To address a wide range of molar peptide/lipid ratios between 1:3000 and 1:8, multilayers of hydrated DMPC containing a 19F-labeled peptide were oriented between stacked glass plates. Maintaining an approximately constant amount of peptide gives rise to thick samples (18 plates) at low, and thin samples (3 plates) at high peptide/lipid ratio. Accurate referencing was critical to reveal a small but significant change over 5 ppm in the anisotropic chemical shift of the 19F label on the peptide, indicative of a change in the orientation and/or dynamics of PGLa in the membrane.     

Neutronenbeugungsuntersuchungen der magnetischen Struktur von TmCo3

The magnetic structure of the intermetallic TmCo₃ compound, determined by neutron diffraction measurements at 4.2 K on a powder sample, is colinear to the hexagonal c-axis, with the magnetic moments of Tm- and Co-ions being antiparallel coupled. The saturation moments have been found to beµ(Tm)=6.5µ _B andµ(Co)=0.8µ _B . The calculated magnetic moment of the Tm-ion by crystal field theory, based on a point charge model, is that of the free Tm³⁺ ion.