Dispersion approach to real and virtual Compton scattering

In recent years, new precision experiments have become possible withthe high luminosity accelerator facilities at MAMIand JLab, supplyingphysicists with precision data sets for different hadronic reactions inthe intermediate energy region, such as pion photo- andelectroproduction and real and virtual Compton scattering.By means of the low energy theorem (LET), the global properties of thenucleon (its mass, charge, and magnetic moment) can be separated fromthe effects of the internal structure of the nucleon, which areeffectively described by polarizabilities. Thepolarizabilities quantify the deformation of the charge andmagnetization densities inside the nucleon in an applied quasistaticelectromagnetic field. The present work is dedicated to develop atool for theextraction of the polarizabilities from these precise Compton data withminimum model dependence, making use of the detailed knowledge of pionphotoproduction by means of dispersion relations (DR). Due to thepresence of t-channel poles, the dispersion integrals for two ofthe six Compton amplitudes diverge. Therefore, we have suggested to subtract the s-channel dispersion integrals at zero photon energy($nu=0$). The subtraction functions at $nu=0$ are calculated through DRin the momentum transfer t at fixed $nu=0$, subtracted at t=0. For this calculation, we use the information about the t-channel process, $gammagammatopipito Nbar{N}$. In this way, four of thepolarizabilities can be predicted using the unsubtracted DR in the $s$-channel. The other two, $alpha-beta$ and $gamma_pi$, are free parameters in ourformalism and can be obtained from a fit to the Compton data.We present the results for unpolarized and polarized RCS observables,%in the kinematics of the most recent experiments, and indicate anenhanced sensitivity to the nucleon polarizabilities in theenergy range between pion production threshold and the $Delta(1232)$-resonance.newlineindentFurthermore,we extend the DR formalism to virtual Compton scattering (radiativeelectron scattering off the nucleon), in which the concept of thepolarizabilities is generalized to the case of avirtual initial photon by introducing six generalizedpolarizabilities (GPs). Our formalism provides predictions for the fourspin GPs, while the two scalar GPs $alpha(Q^2)$ and $beta(Q^2)$ have to befitted to the experimental data at each value of $Q^2$.We show that at energies betweenpion threshold and the $Delta(1232)$-resonance position, thesensitivity to the GPs can be increased significantly, as compared tolow energies, where the LEX is applicable. Our DR formalism can be used for analysing VCS experiments over a widerange of energy and virtuality $Q^2$, which allows one to extract theGPs from VCS data in different kinematics with a minimum of model dependence.

Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Entwicklung der zeitaufgelösten Photoemissions-Elektronenmikroskopie für die Untersuchung der Magnetisierungsdynamik von mikrostrukturierten magnetischen Schichten

Im Rahmen dieser Arbeit wurde die zeitaufgelöste Photoemissions Elektronenmikroskopie (TR-PEEM) für die in-situ Untersuchung ultraschneller dynamischer Prozesse in dünnen mikrostrukturierten magnetischen Schichten während eines rasch verändernden externen Magnetfelds entwickelt. Das Experiment basiert auf der Nutzung des XMCD-Kontrasts (X-ray magnetic circular dichroism) mit Hilfe des zirkularpolarisierten Lichts von Synchrotronstrahlungsquellen (Elektronenspeicherringen BESSY II (Berlin) und ESRF (Grenoble)) für die dynamische Darstellung der magnetischen Domänen während ultraschneller Magnetisierungsvorgänge. Die hier entwickelte Methode wurde als erfolgreiche Kombination aus einer hohen Orts- und Zeitauflösung (weniger als 55 nm bzw. 15 ps) realisiert. Mit der hier beschriebenen Methode konnte nachgewiesen werden, dass die Magnetisierungsdynamik in großen Permalloy-Mikrostrukturen (40 µm x 80 µm und 20 µm x 80 µm, 40 nm dick) durch inkohärente Drehung der Magnetisierung und mit der Bildung von zeitlich abhängigen Übergangsdomänen einher geht, die den Ummagnetisierungsvorgang blockieren. Es wurden neue markante Differenzen zwischen der magnetischen Response einer vorgegebenen Dünnfilm-Mikrostruktur auf ein gepulstes externes Magnetfeld im Vergleich zu dem quasi-statischen Fall gefunden. Dies betrifft die Erscheinung von transienten raumzeitlichen Domänenmustern und besonderen Detailstrukturen in diesen Mustern, welche im quasi-statischen Fall nicht auftreten. Es wurden Beispiele solcher Domänenmuster in Permalloy-Mikrostrukturen verschiedener Formen und Größen untersucht und diskutiert. Insbesondere wurde die schnelle Verbreiterung von Domänenwänden infolge des präzessionalen Magnetisierungsvorgangs, die Ausbildung von transienten Domänenwänden und transienten Vortizes sowie die Erscheinung einer gestreiften Domänenphase aufgrund der inkohärenten Drehung der Magnetisierung diskutiert. Ferner wurde die Methode für die Untersuchung von stehenden Spinwellen auf ultradünnen (16 µm x 32 µm groß und 10 nm dick) Permalloy-Mikrostrukturen herangezogen. In einer zum periodischen Anregungsfeld senkrecht orientierten rechteckigen Mikrostruktur wurde ein induziertes magnetisches Moment gefunden. Dieses Phänomen wurde als „selbstfangende“ Spinwellenmode interpretiert. Es wurde gezeigt, dass sich eine erzwungene Normalmode durch Verschiebung einer 180°-Néelwand stabilisiert. Wird das System knapp unterhalb seiner Resonanzfrequenz angeregt, passt sich die Magnetisierungsverteilung derart an, dass ein möglichst großer Teil der durch das Anregungsfeld eingebrachten Energie im System verbleibt. Über einem bestimmten Grenzwert verursacht die Spinwellenmode nahe der Resonanzfrequenz eine effektive Kraft senkrecht zur 180°-Néel-Wand. Diese entsteht im Zentrum der Mikrostruktur und wird durch die streufeldinduzierte Kraft kompensiert. Als zusätzliche Möglichkeit wurden die Streufelder von magnetischen Mikrostrukturen während der dynamischen Prozesse quantitativ bestimmt und das genaue zeitliche Profil des Streufelds untersucht. Es wurde gezeigt, dass das zeitaufgelöste Photoemissions Elektronenmikroskop als ultraschnelles oberflächensensitives Magnetometer eingesetzt werden kann.

Direct observation of a single proton in a Penning trap

In der vorgelegten Doktorarbeit werden Experimente vorgestellt, die an einem einzelnen Proton in einer Penningfalle durchgeführt worden sind. Die Eigenbewegung eines isoliert gespeicherten, freien Protons konnte elektronisch durch Kopplung an einen Resonanzschwingkreis nachgewiesen werden. Dies stellt eine nicht-destruktive Messung dar, d. h. das Teilchen geht während der Messung nicht verloren. Die freie Zyklotronfrequenz, die aus den drei gemessenen Eigenfrequenzen hervorgeht, ist eine von zwei zur Bestimmung des magnetischen Moments notwendigen Frequenzen. So wird im Gegensatz zu den existierenden Arbeiten eine direkte Bestimmung des g-Faktors ermöglicht. Planung, Entwicklung und Inbetriebnahme des experimentellen Aufbaus wurden im Rahmen dieser Arbeit durchgeführt, womit eine Messgenauigkeit von 10-7 erreicht wurde. Die dabei zu bewältigenden technischen Herausforderungen zur Bestimmung der zweiten Frequenz (der Larmorfrequenz) ergeben sich aus der Kleinheit des magnetischen Moments. Bei dem für diese Messung benötigten Spinzustand des Teilchens handelt es sich um einen internen Freiheitsgrad, der nur über eine Kopplung des magnetischen Moments an die Eigenbewegung bestimmt werden kann. Eine neuartige, hybride Penningfalle wird in dieser Arbeit vorgestellt, die als Quantensprung-Spektrometer die Spininformation auf die Eigenbewegung abbildet. Damit liegt der aus der magnetischen Kopplung resultierende Frequenzunterschied in den beiden Spinzuständen erstmalig in einem elektronisch detektierbaren Bereich.

Unconventional correlated systems

This work comprises three different types of unconventional correlated systems.rnChapters 3-5 of this work are about the open shell compounds Rb4O6 and Cs4O6. These mixed valent compounds contain oxygen in two different modifications: the closed-shell peroxide anion is nonmagnetic, whereas the hyperoxide anion contains an unpaired electrons in an antibonding pi*-orbital. Due to this electron magnetic ordering is rendered possible. In contrast to theoretical predictions, which suggested half-metallic ferromagnetism for Rb4O6,rndominating antiferromagnetic interactions were found in the experiment. Besidesrna symmetry reduction due to the mixed valency, strong electronic correlations of this highly molecular system determine its properties; it is a magnetically frustrated insulator. The corresponding Cs4O6 was found to show similar properties.rnChapters 6-9 of this work are about intermetallic Heusler superconductors. rnAll of these superconductors were rationally designed using the van Hove scenario as a working recipe. A saddle point in the energy dispersion curve of a solid leads to a van Hove singularity in the density of states. In the Ni-based and Pd-based Heusler superconductors presented in this work this sort of a valence instability occurs at the high-symmetry L point and coincides or nearly coincides with the Fermi level. The compounds escape the high density of states at the Fermi energy through a transition into the correlated superconducting state.rnChapter 10 of this work is about the tetragonally distorted ferrimagnetic DO22 phase of Mn3Ga. This hard-magnetic modification is technologically useful for spin torque transfer applications. The phase exhibits two different crystallographic sites that are occupied by Mn atoms and can thus be written as Mn2MnGa. The competition between the mainly itinerant moments of the Mn atoms at the Wyckoff position 4d and the localized moments of the Mn atoms at the Wyckoff position 2b leads to magnetic correlations. The antiferromagnetic orientation of these moments determines the compound to exhibit a resulting magnetic moment of approximately 1 µB per formula unit in a partially compensated ferrimagnetic configuration.

Measurement of the e + e - pi + pi - pi + pi - cross section using initial state radiation at BABAR

One of the most precisely measured quantities in particle physics is the magnetic moment of the muon, which describes its coupling to an external magnetic field. It is expressed in form of the anomalous magnetic moment of the muon a_mu=(g_mu-2)/2 and has been determined experimentally with a precision of 0.5 parts per million. The current direct measurement and the theoretical prediction of the standard model differ by more than 3.5 standard deviations. Concerning theory, the contribution of the QED and weak interaction to a_mu can be calculated with very high precision in a perturbative approach.rnAt low energies, however, perturbation theory cannot be used to determine the hadronic contribution a^had_mu. On the other hand, a^had_mu may be derived via a dispersion relation from the sum of measured cross sections of exclusive hadronic reactions. Decreasing the experimental uncertainty on these hadronic cross sections is of utmost importance for an improved standard model prediction of a_mu.rnrnIn addition to traditional energy scan experiments, the method of Initial State Radiation (ISR) is used to measure hadronic cross sections. This approach allows experiments at colliders running at a fixed centre-of-mass energy to access smaller effective energies by studying events which contain a high-energetic photon emitted from the initial electron or positron. Using the technique of ISR, the energy range from threshold up to 4.5GeV can be accessed at Babar.rnrnThe cross section e+e- -> pi+pi- contributes with approximately 70% to the hadronic part of the anomalous magnetic moment of the muon a_mu^had. This important channel has been measured with a precision of better than 1%. Therefore, the leading contribution to the uncertainty of a_mu^had at present stems from the invariant mass region between 1GeV and 2GeV. In this energy range, the channels e+e- -> pi+pi-pi+pi- and e+e- -> pi+pi-pi0pi0 dominate the inclusive hadronic cross section. The measurement of the process e+e- -> pi+pi-pi+pi- will be presented in this thesis. This channel has been previously measured by Babar based on 25% of the total dataset. The new analysis includes a more detailed study of the background contamination from other ISR and non-radiative background reactions. In addition, sophisticated studies of the track reconstruction as well as the photon efficiency difference between the data and the simulation of the Babar detector are performed. With these auxiliary studies, a reduction of the systematic uncertainty from 5.0% to 2.4% in the peak region was achieved.rnrnThe pi+pi-pi+pi- final state has a rich internal structure. Hints are seen for the intermediate states rho(770)^0 f_2(1270), rho(770)^0 f_0(980), as well as a_1(1260)pi. In addition, the branching ratios BR(jpsi -> pi+pi-pi+pi-) and BR(psitwos -> jpsi pi+pi-) are extracted.rn

Der g-Faktor des Protons

In dieser Arbeit wird die bisher präziseste und erste direkte Hochpräzisionsmessung des g-Faktors eines einzelnen Protons präsentiert. Die Messung beruht auf der nicht-destruktiven Bestimmung der Zyklotronfrequenz und der Larmorfrequenz eines in einer Penning-Falle gespeicherten Protons. Zur Bestimmung der Larmorfrequenz wird die Spin-Flip-Wahrscheinlichkeit als Funktion einer externen Spin-Flip-Anregung aufgenommen. Zu diesem Zweck wird der kontinuierliche Stern-Gerlach Effekt verwendet, welcher zu einer Kopplung des Spin-Moments an die axiale Bewegung des Protons führt. Ein Spin-Flip zeigt sich dabei in einem Sprung der axialen Bewegungsfrequenz. Die Schwierigkeit besteht darin, diesen Frequenzsprung auf einem Hintergrund axialer Frequenzfluktuationen zu detektieren. Um diese Herausforderung zu bewältigen, wurden neuartige Methoden und Techniken angewandt. Zum einen wurden supraleitende Nachweise mit höchster Empfindlichkeit entwickelt, welche schnelle und damit präzise Frequenzmessungen erlauben. Zum anderen wurde eine auf dem statistischen Bayes Theorem basierende Spin-Flip-Analyse-Methode angewandt. Mit diesen Verbesserungen war es möglich, einzelne Spin-Flips eines einzelnen Protons zu beobachten. Dies wiederum ermöglichte die Anwendung der sogenannten Doppelfallen-Methode, und damit die eingangs erwähnte Messung des g-Faktors mit einer Präzision von 4.3 10^-9.

Virtual photon-photon scattering

Based on analyticity, unitarity, and Lorentz invariance the contribution from hadronic vacuum polarization to the anomalous magnetic moment of the muon is directly related to the cross section of e+e− → hadrons. We review the main difficulties that impede such an approach for light-by-light scattering and identify the required ingredients from experiment. Amongst those, the most critical one is the scattering of two virtual photons into meson pairs. We analyze the analytic structure of the process γ*γ* → ππ and show that the usual Muskhelishvili–Omnès representation can be amended in such a way as to remain valid even in the presence of anomalous thresholds.

Magnetic properties and chemical composition at DSDP Hole 77-538A

Magnetic properties of doleritic and some metamorphic basement rocks underlying Catoche Knoll are studied. Doleritic rocks show a high saturation magnetic moment (2-5 emu/g) compared to metamorphic rocks (0.1-1 emu/g). Magnetic minerals of rocks from this hole show a high stability when heated in vacuo up to 600°C at a fixed rate of heating. Curie temperatures are distributed close to 550°C. These properties differ markedly from those of common submarine basalts observed before. X-ray microprobe analysis techniques were used to determine internal structures of ferromagnetic minerals; in most of ferromagnetic minerals there exist two different types of magnetic phases (i.e., products of high-temperature and low-temperature oxidations). Interpretations on the coexisting, seemingly contradictory, phases can be made based upon present analyses.

Paleomagnetic and rock magnetic properties of IODP Expedition 318 cores

The Integrated Ocean Drilling Program Expedition 318 to the Wilkes Land margin of Antarctica recovered a sedimentary succession ranging in age from lower Eocene to the Holocene. Excellent stratigraphic control is key to understanding the timing of paleoceanographic events through critical climate intervals. Drill sites recovered the lower and middle Eocene, nearly the entire Oligocene, the Miocene from about 17 Ma, the entire Pliocene and much of the Pleistocene. The paleomagnetic properties are generally suitable for magnetostratigraphic interpretation, with well-behaved demagnetization diagrams, uniform distribution of declinations, and a clear separation into two inclination modes. Although the sequences were discontinuously recovered with many gaps due to coring, and there are hiatuses from sedimentary and tectonic processes, the magnetostratigraphic patterns are in general readily interpretable. Our interpretations are integrated with the diatom, radiolarian, calcareous nannofossils and dinoflagellate cyst (dinocyst) biostratigraphy. The magnetostratigraphy significantly improves the resolution of the chronostratigraphy, particularly in intervals with poor biostratigraphic control. However, Southern Ocean records with reliable magnetostratigraphies are notably scarce, and the data reported here provide an opportunity for improved calibration of the biostratigraphic records. In particular, we provide a rare magnetostratigraphic calibration for dinocyst biostratigraphy in the Paleogene and a substantially improved diatom calibration for the Pliocene. This paper presents the stratigraphic framework for future paleoceanographic proxy records which are being developed for the Wilkes Land margin cores. It further provides tight constraints on the duration of regional hiatuses inferred from seismic surveys of the region.

Low-temperature magnetic remanence and hysteresis measurements on sediment core GeoB4901-8 from the Niger deep-sea fan

Low-temperature (LT) magnetic remanence and hysteresis measurements, in the range 300-5 K, were combined with energy dispersive spectroscopy (EDS) in order to characterize the magnetic inventory of strongly diagenetically altered sediments originating from the Niger deep-sea fan. We demonstrate the possibility of distinguishing between different compositions of members of the magnetite-ulvöspinel and ilmenite-hematite solid solution series on a set of five representative samples, two from the upper suboxic and three from the lower sulfidic anoxic zone of gravity core GeoB 4901. Highly sensitive LT magnetic measurements were performed on magnetic extracts resulting in large differences in the magnetic behavior between samples from the different layers. This emphasizes that both Fe-Ti oxide phases occur in different proportions in the two geochemical environments. Most prominent are variations in the coercivity sensitive parameter coercive field (BC). At room-temperature (RT) hysteresis loops for all extracts are narrow and yield low coercivities (6-13 mT). With decreasing temperature the loops become more pronounced and wider. At 5 K an approximately 5-fold increase in BC for the suboxic samples contrasts a 20-25-fold increase for the samples from the anoxic zone. We demonstrate that this distinct increase in BC at LT corresponds to the increasing proportion of the Ti-rich hemoilmenite phase, while Fe-rich (titano-)magnetite dominates the magnetic signal at RT. This trend is also seen in the room-temperature saturation isothermal remanent magnetization (RT-SIRM) cycles: suboxic samples show remanence curves dominated by Fe-rich mineral phases while anoxic samples display curves clearly dominated by Ti-rich particles. We show that the EDS intensity ratios of the characteristic Fe Kalpha and Ti Kalpha lines of the Fe-Ti oxides may be used to differentiate between members of the magnetite-ulvöspinel and ilmenite-hematite solid solution series. Furthermore it is possible to calculate an approximate composition for each grain if the intensity ratios of natural particles are linked to well-known standards. Thus, element spectra with high Fe/Ti intensity ratios were found to be rather typical of titanomagnetite while low Fe/Ti ratios are indicative of hemoilmenite. The EDS analyses confirm the LT magnetic results, Fe-rich magnetic phases dominate in the upper suboxic environment whereas Ti-rich magnetic phases comprise the majority of particles in the lower anoxic domain: The mineral assemblage of the upper suboxic environments is composed of magnetite (~19%), titanomagnetite (~62%), hemoilmenite (~17%) and ~2% other particles. In the lower anoxic sediments, reductive diagenetic alteration has resulted in more extensive depletion of the (titano-)magnetite phase, resulting in a relative enrichment of the hemoilmenite phase (~66%). In these strongly anoxic sediments stoichiometric magnetite is barely preserved and only ~5% titanomagnetite was detected. The remaining ~28% comprises Ti-rich particles such as pseudobrookite or rutile.