Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps

The g-factor is a constant which connects the magnetic moment $vec{mu}$ of a charged particle, of charge q and mass m, with its angular momentum $vec{J}$. Thus, the magnetic moment can be writen $ vec{mu}_J=g_Jfrac{q}{2m}vec{J}$. The g-factor for a free particle of spin s=1/2 should take the value g=2. But due to quantum electro-dynamical effects it deviates from this value by a small amount, the so called g-factor anomaly $a_e$, which is of the order of $10^{-3}$ for the free electron. This deviation is even bigger if the electron is exposed to high electric fields. Therefore highly charged ions, where electric field strength gets values on the order of $10^{13}-10^{16}$V/cm at the position of the bound electron, are an interesting field of investigations to test QED-calculations. In previous experiments [H"aff00,Ver04] using a single hydrogen-like ion confined in a Penning trap an accuracy of few parts in $10^{-9}$ was obtained. In the present work a new method for precise measurement of magnetic the electronic g-factor of hydrogen-like ions is discussed. Due to the unavoidable magnetic field inhomogeneity in a Penning trap, a very important contribution to the systematic uncertainty in the previous measurements arose from the elevated energy of the ion required for the measurement of its motional frequencies. Then it was necessary to extrapolate the result to vanishing energies. In the new method the energy in the cyclotron degree of freedom is reduced to the minimum attainable energy. This method consist in measuring the reduced cyclotron frequency $nu_{+}$ indirectly by coupling the axial to the reduced cyclotron motion by irradiation of the radio frequency $nu_{coup}=nu_{+}-nu_{ax}+delta$ where $delta$ is, in principle, an unknown detuning that can be obtained from the knowledge of the coupling process. Then the only unknown parameter is the desired value of $nu_+$. As a test, a measurement with, for simplicity, artificially increased axial energy was performed yielding the result $g_{exp}=2.000~047~020~8(24)(44)$. This is in perfect agreement with both the theoretical result $g_{theo}=2.000~047~020~2(6)$ and the previous experimental result $g_{exp1}=2.000~047~025~4(15)(44).$ In the experimental results the second error-bar is due to the uncertainty in the accepted value for the electron's mass. Thus, with the new method a higher accuracy in the g-factor could lead by comparison to the theoretical value to an improved value of the electron's mass. [H"af00] H. H"affner et al., Phys. Rev. Lett. 85 (2000) 5308 [Ver04] J. Verd'u et al., Phys. Rev. Lett. 92 (2004) 093002-1

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Interplay of pi–pi stacking and hydrogen bonding in conjugated supramolecular systems studied by solid-state NMR

In this work supramolecular organic systems based on rigid pi-conjugated building blocks and flexible side chains were studied via solid-state NMR spectroscopy. Specifically, these studies focussed on phenylene ethynylene based macrocycles, polymer systems including polythiophenes, and rod-coil copolymers of oligo(p-benzamide) and poly(ethylene glycol). All systems were studied in terms of the local order and mobility. The central topic of this dissertation was to elucidate the role of the flexible side chains in interplay of different non-covalent interactions, like pi-pi-stacking and hydrogen bonding.Combining the results of this work, it can be concluded that the ratio of the rigid block and the attached alkyl side chains can be crucial for the design of an ordered pi-conjugated supramolecular system. Through alkyl side chains, it is also possible to introduce liquid-crystalline phases in the system, which can foster the local order of the system. Moreover in the studied system longer, unbranched alkyl side chains are better suited to stabilize the corresponding aggregation than shorter, branched ones.The combination of non-covalent interactions such as pi-pi-stacking and hydrogen bonding play an important role for structure formation. However, the effect of pi-pi-stacking interaction is much weaker than the effect of hydrogen bonding and is only observed in systems with a suitable local order. Hence, they are often not strong enough to control the local order. In contrast, hydrogen bonds predominantly influence the structural organization and packing. In comparison the size of the alkyl side chains is only of minor importance. The suppression of certain hydrogen bonds can lead to completely different structures and can induce a specific aggregation behavior. Thus, for the design of a supramolecular ordered system the presence of hydrogen bonding efficiently stabilizes the corresponding structure, but the ratio of hydrogen bond forming groups should be kept low to be able to influence the structure selectively.

Ab-initio study of hydrogen technology materials for hydrogen storage and proton conduction

This dissertation deals with two specific aspects of a potential hydrogen-based energy economy, namely the problems of energy storage and energy conversion. In order to contribute to the solution of these problems, the structural and dynamical properties of two promising materials for hydrogen storage (lithium imide/amide) and proton conduction (poly[vinyl phosphonic acid]) are modeled on an atomistic scale by means of first principles molecular dynamics simulation methods.rnrnrnIn the case of the hydrogen storage system lithium amide/imide (LiNH_2/Li_2NH), the focus was on the interplay of structural features and nuclear quantum effects. For these calculations, Path-Integral Molecular Dynamics (PIMD) simulations were used. The structures of these materials at room temperature were elucidated; in collaboration with an experimental group, a very good agreement between calculated and experimental solid-state 1H-NMR chemical shifts was observed. Specifically, the structure of Li_2NH features a disordered arrangement of the Li lattice, which was not reported in previous studies. In addition, a persistent precession of the NH bonds was observed in our simulations. We provide evidence that this precession is the consequence of a toroid-shaped effective potential, in which the protons in the material are immersed. This potential is essentially flat along the torus azimuthal angle, which might lead to important quantum delocalization effects of the protons over the torus.rnrnOn the energy conversion side, the dynamics of protons in a proton conducting polymer (poly[vinyl phosphonic acid], PVPA) was studied by means of a steered ab-initio Molecular Dynamics approach applied on a simplified polymer model. The focus was put on understanding the microscopic proton transport mechanism in polymer membranes, and on characterizing the relevance of the local environment. This covers particularly the effect of water molecules, which participate in the hydrogen bonding network in the material. The results indicate that these water molecules are essential for the effectiveness of proton conduction. A water-mediated Grotthuss mechanism is identified as the main contributor to proton conduction, which agrees with the experimentally observed decay on conductivity for the same material in the absence of water molecules.rnrnThe gain in understanding the microscopic processes and structures present in this materials can help the development of new materials with improved properties, thus contributing to the solution of problems in the implementation of fuel cells.

Analysis of diffractive dissociation of K - into K - pi + pi - on a liquid hydrogen target at the COMPASS spectrometer

The systematic exploration of excited meson and baryon states was the central topic of the COMPASS physics program in the years 2008 and 2009 at the CERN facility. A hadron beam of 190 GeV/c particle momentum was impinging on a 40 cm long liquid hydrogen target to create excited states of beam particles by diffractive processes. The presented work is about the study of the process $K^- p rightarrow K^- pi^+ pi^- p_{recoil}$ where special emphasis is put on how kaons were distinguished from pions with the CEDAR detectors in the initial channel as well as with the RICH detector in the final states. At the end formed 270 000 events an invariant K pi pi mass distribution of overlapping resonances. In addition a detailed MC simulation study of 44 million decays in the range of 0.8 < m(K pi pi) [GeV/c^2] < 3.0 was performed and analysed for acceptance corrections.All information was combined into a mass independent partial wave analysis to observe resonances of individual particles. The main contribution was found in the JP = 0+, 1+, 2- and 2+ spin-parity states.

Variational Monte Carlo study of the hydrogen electronic structure at ultra-high pressure

Die causa finalis der vorliegenden Arbeit ist das Verständnis des Phasendiagramms von Wasserstoff bei ultrahohen Drücken, welche von nichtleitendem H2 bis hin zu metallischem H reichen. Da die Voraussetzungen für ultrahohen Druck im Labor schwer zu schaffen sind, bilden Computersimulationen ein wichtiges alternatives Untersuchungsinstrument. Allerdings sind solche Berechnungen eine große Herausforderung. Eines der größten Probleme ist die genaue Auswertung des Born-Oppenheimer Potentials, welches sowohl für die nichtleitende als auch für die metallische Phase geeignet sein muss. Außerdem muss es die starken Korrelationen berücksichtigen, die durch die kovalenten H2 Bindungen und die eventuellen Phasenübergänge hervorgerufen werden. Auf dieses Problem haben unsere Anstrengungen abgezielt. Im Kontext von Variationellem Monte Carlo (VMC) ist die Shadow Wave Function (SWF) eine sehr vielversprechende Option. Aufgrund ihrer Flexibilität sowohl lokalisierte als auch delokalisierte Systeme zu beschreiben sowie ihrer Fähigkeit Korrelationen hoher Ordnung zu berücksichtigen, ist sie ein idealer Kandidat für unsere Zwecke. Unglücklicherweise bringt ihre Formulierung ein Vorzeichenproblem mit sich, was die Anwendbarkeit limitiert. Nichtsdestotrotz ist es möglich diese Schwierigkeit zu umgehen indem man die Knotenstruktur a priori festlegt. Durch diesen Formalismus waren wir in der Lage die Beschreibung der Elektronenstruktur von Wasserstoff signifikant zu verbessern, was eine sehr vielversprechende Perspektive bietet. Während dieser Forschung haben wir also die Natur des Vorzeichenproblems untersucht, das sich auf die SWF auswirkt, und dabei ein tieferes Verständnis seines Ursprungs erlangt. Die vorliegende Arbeit ist in vier Kapitel unterteilt. Das erste Kapitel führt VMC und die SWF mit besonderer Ausrichtung auf fermionische Systeme ein. Kapitel 2 skizziert die Literatur über das Phasendiagramm von Wasserstoff bei ultrahohem Druck. Das dritte Kapitel präsentiert die Implementierungen unseres VMC Programms und die erhaltenen Ergebnisse. Zum Abschluss fasst Kapitel 4 unsere Bestrebungen zur Lösung des zur SWF zugehörigen Vorzeichenproblems zusammen.