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

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

The future goal of modern physics is the discovery of physics beyond the Standard Model. One of the most significant hints for New Physics can be seen in the anomalous magnetic moment of the muon - one of the most precise measured variables in modern physics and the main motivation of this work. This variable is associated with the coupling of the muon, an elementary particle, to an external electromagnetic field and is defined as a = (g - 2)/2, whereas g is the gyromagnetic factor of the muon. The muon anomaly has been measured with a relative accuracy of 0.5·10-6. However, a difference between the direct measurement and the Standard Model prediction of 3.6 standard deviations can be observed. This could be a hint for the existence of New Physics. Unfortunately, it is, yet, not significant enough to claim an observation and, thus, more precise measurements and calculations have to be performed.rnThe muon anomaly has three contributions, whereas the ones from quantum electrodynamics and weak interaction can be determined from perturbative calculations. This cannot be done in case of the hadronic contributions at low energies. The leading order contribution - the hadronic vacuum polarization - can be computed via a dispersion integral, which needs as input hadronic cross section measurements from electron-positron annihilations. Hence, it is essential for a precise prediction of the muon anomaly to measure these hadronic cross sections, σ(e+e-→hadrons), with high accuracy. With a contribution of more than 70%, the final state containing two charged pions is the most important one in this context.rnIn this thesis, a new measurement of the σ(e+e-→π+π-) cross section and the pion form factor is performed with an accuracy of 0.9% in the dominant ρ(770) resonance region between 600 and rn900 MeV at the BESIII experiment. The two-pion contribution to the leading-order (LO) hadronic vacuum polarization contribution to (g - 2) from the BESIII result, obtained in this work, is computed to be a(ππ,LO,600-900 MeV) = (368.2±2.5stat±3.3sys)·10-10. With the result presented in this thesis, we make an important contribution on the way to solve the (g - 2) puzzle.

Light-by-light scattering and muon’s anomalous magnetic moment

A study of hadron production by photons opens unique ways to address a number of fundamental problems in strong interaction physics as well as fundamental questions in Quantum Field Theory. In particular, an understanding of two-photon processes is of crucial importance for constraining the hadronic uncertainties in precision measurements and in searches for new physics. The process of

The g-factor of the electron bound in 28 Si 13+ : the most stringent test of bound-state quantum electrodynamics

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike 28Si13+. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision.rnThe development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 40 ppt, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.

Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.

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

Magnetic properties of selected 3d- and 4f-systems on alpha-Al 2 O 3 substrates

In this work the growth and the magnetic properties of the transition metals molybdenum, niobium, and iron and of the highly-magnetostrictive C15 Laves phases of the RFe2 compounds (R: Rare earth metals: here Tb, Dy, and Tb{0.3}Dy{0.7} deposited on alpha-Al2O3 (sapphire) substrates are analyzed. Next to (11-20) (a-plane) oriented sapphire substrates mainly (10-10) (m-plane) oriented substrates were used. These show a pronounced facetting after high temperature annealing in air. Atomic force microscopy (AFM) measurements reveal a dependence of the height, width, and angle of the facets with the annealing temperature. The observed deviations of the facet angles with respect to the theoretical values of the sapphire (10-1-2) and (10-11) surfaces are explained by cross section high resolution transmission electron microscopy (HR-TEM) measurements. These show the plain formation of the (10-11) surface while the second, energy reduced (10-1-2) facet has a curved shape given by atomic steps of (10-1-2) layers and is formed completely solely at the facet ridges and valleys. Thin films of Mo and Nb, respectively, deposited by means of molecular beam epitaxy (MBE) reveal a non-twinned, (211)-oriented epitaxial growth as well on non-faceted as on faceted sapphire m-plane, as was shown by X-Ray and TEM evaluations. In the case of faceted sapphire the two bcc crystals overgrow the facets homogeneously. Here, the bcc (111) surface is nearly parallel to the sapphire (10-11) facet and the Mo/Nb (100) surface is nearly parallel to the sapphire (10-1-2) surface. (211)-oriented Nb templates on sapphire m-plane can be used for the non-twinned, (211)-oriented growth of RFe2 films by means of MBE. Again, the quality of the RFe2 films grown on faceted sapphire is almost equal to films on the non-faceted substrate. For comparison thin RFe2 films of the established (110) and (111) orientation were prepared. Magnetic and magnetoelastic measurements performed in a self designed setup reveal a high quality of the samples. No difference between samples with undulated and flat morphology can be observed. In addition to the preparation of covering, undulating thin films on faceted sapphire m-plane nanoscopic structures of Nb and Fe were prepared by shallow incidence MBE. The formation of the nanostructures can be explained by a shadowing of the atomic beam due to the facets in addition to de-wetting effects of the metals on the heated sapphire surface. Accordingly, the nanostructures form at the facet ridges and overgrow them. The morphology of the structures can be varied by deposition conditions as was shown for Fe. The shape of the structures vary from pearl-necklet strung spherical nanodots with a diameter of a few 10 nm to oval nanodots of a few 100 nm length to continuous nanowires. Magnetization measurements reveal uniaxial magnetic anisotropy with the easy axis of magnetization parallel to the facet ridges. The shape of the hysteresis is depending on the morphology of the structures. The magnetization reversal processes of the spherical and oval nanodots were simulated by micromagnetic modelling and can be explained by the formation of magnetic vortices.

Tuning the structural and magnetic properties of Sr 2 FeReO 6 by substituting Fe and Re with valence invariant metals

In the course of this work the effect of metal substitution on the structural and magnetic properties of the double perovskites Sr2MM’O6 (M = Fe, substituted by Cr, Zn and Ga; M’ = Re, substituted by Sb) was explored by means of X-ray diffraction, magnetic measurements, band structure calculations, Mößbauer spectroscopy and conductivity measurements. The focus of this study was the determination of (i) the kind and structural boundary conditions of the magnetic interaction between the M and M’ cations and (ii) the conditions for the principal application of double perovskites as spintronic materials by means of the band model approach. Strong correlations between the electronic, structural and magnetic properties have been found during the study of the double perovskites Sr2Fe1-xMxReO6 (0 < x < 1, M = Zn, Cr). The interplay between van Hove-singularity and Fermi level plays a crucial role for the magnetic properties. Substitution of Fe by Cr in Sr2FeReO6 leads to a non-monotonic behaviour of the saturation magnetization (MS) and an enhancement for substitution levels up to 10 %. The Curie temperatures (TC) monotonically increase from 401 to 616 K. In contrast, Zn substitution leads to a continuous decrease of MS and TC. The diamagnetic dilution of the Fe-sublattice by Zn leads to a transition from an itinerant ferrimagnetic to a localized ferromagnetic material. Thus, Zn substitution inhibits the long-range ferromagnetic interaction within the Fe-sublattice and preserves the long-range ferromagnetic interaction within the Re-sublattice. Superimposed on the electronic effects is the structural influence which can be explained by size effects modelled by the tolerance factor t. In the case of Cr substitution, a tetragonal – cubic transformation for x > 0.4 is observed. For Zn substituted samples the tetragonal distortion linearly increases with increasing Zn content. In order to elucidate the nature of the magnetic interaction between the M and M’ cations, Fe and Re were substituted by the valence invariant main group metals Ga and Sb, respectively. X-ray diffraction reveals Sr2FeRe1-xSbxO6 (0 < x < 0.9) to crystallize without antisite disorder in the tetragonal distorted perovskite structure (space group I4/mmm). The ferrimagnetic behaviour of the parent compound Sr2FeReO6 changes to antiferromagnetic upon Sb substitution as determined by magnetic susceptibility measurements. Samples up to a doping level of 0.3 are ferrimagnetic, while Sb contents higher than 0.6 result in an overall antiferromagnetic behaviour. 57Fe Mößbauer results show a coexistence of ferri- and antiferromagnetic clusters within the same perovskite-type crystal structure in the Sb substitution range 0.3 < x < 0.8, whereas Sr2FeReO6 and Sr2FeRe0.9Sb0.1O6 are “purely” ferrimagnetic and Sr2FeRe0.1Sb0.9O6 contains antiferromagnetically ordered Fe sites only. Consequently, a replacement of the Re atoms by a nonmagnetic main group element such as Sb blocks the double exchange pathways Fe–O–Re(Sb)–O–Fe along the crystallographic axis of the perovskite unit cell and destroys the itinerant magnetism of the parent compound. The structural and magnetic characterization of Sr2Fe1-xGaxReO6 (0 < x < 0.7) exhibit a Ga/Re antisite disorder which is unexpected because the parent compound Sr2FeReO6 shows no Fe/Re antisite disorder. This antisite disorder strongly depends on the Ga content of the sample. Although the X-ray data do not hint at a phase separation, sample inhomogeneities caused by a demixing are observed by a combination of magnetic characterization and Mößbauer spectroscopy. The 57Fe Mößbauer data suggest the formation of two types of clusters, ferrimagnetic Fe- and paramagnetic Ga-based ones. Below 20 % Ga content, Ga statistically dilutes the Fe–O–Re–O–Fe double exchange pathways. Cluster formation begins at x = 0.2, for 0.2 < x < 0.4 the paramagnetic Ga-based clusters do not contain any Fe. Fe containing Ga-based clusters which can be detected by Mößbauer spectroscopy firstly appear for x = 0.4.

Concept and realization of the A4 compton backscattering polarimeter at MAMI

The main concern of the A4 parity violation experiment at the Mainzer Microtron accelerator facility is to study the electric and magnetic contributions of strange quarks to the charge and magnetism of the nucleons at the low momentum transfer region. More precisely, the A4 collaboration investigates the strange quarks' contribution to the electric and magnetic vector form factors of the nucleons. Thus, it is important that the A4 experiment uses an adequate and precise non-destructive online monitoring tool for the electron beam polarization when measuring single spin asymmetries in elastic scattering of polarized electrons from unpolarized nucleons. As a consequence, the A4 Compton backscattering polarimeter was designed and installed such that we can take the absolute measurement of the electron beam polarization without interruption to the parity violation experiment. The present study shows the development of an electron beam line that is called the chicane for the A4 Compton backscattering polarimeter. The chicane is an electron beam transport line and provides an interaction region where the electron beam and the laser beam overlap. After studying the properties of beam line components carefully, we developed an electron beam control system that makes a beam overlap between the electron beam and the laser beam. Using the system, we can easily achieve the beam overlap in a short time. The electron control system, of which the performance is outstanding, is being used in production beam times. And the study presents the development of a scintillating fiber electron detector that reduces the statistical error in the electron polarization measurement. We totally redesigned the scintillating fiber detector. The data that were taken during a 2008 beam time shows a huge background suppression, approximately 80 percent, while leaving the Compton spectra almost unchanged when a coincidence between the fiber detector and the photon detector is used. Thus, the statistical error of the polarization measurement is reduced by about 40 percent in the preliminary result. They are the significant progress in measuring a degree of polarization of the electron beam.

Feasibility studies of the pp pi 0 e + e - electromagnetic channel at PANDA

Among all possible realizations of quark and antiquark assembly, the nucleon (the proton and the neutron) is the most stable of all hadrons and consequently has been the subject of intensive studies. Mass, shape, radius and more complex representations of its internal structure are measured since several decades using different probes. The proton (spin 1/2) is described by the electric GE and magnetic GM form factors which characterise its internal structure. The simplest way to measure the proton form factors consists in measuring the angular distribution of the electron-proton elastic scattering accessing the so-called Space-Like region where q2 < 0. Using the crossed channel antiproton proton <--> e+e-, one accesses another kinematical region, the so-called Time-Like region where q2 > 0. However, due to the antiproton proton <--> e+e- threshold q2th, only the kinematical domain q2 > q2th > 0 is available. To access the unphysical region, one may use the antiproton proton --> pi0 e+ e- reaction where the pi0 takes away a part of the system energy allowing q2 to be varied between q2th and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the new high intensity antiproton ring at the FAIR facility at Darmstadt. To describe the antiproton proton --> pi0 e+ e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R = |GE|/|GM| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region up to now. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the antiproton proton --> pi0 pi+ pi- background reaction considered as the most dangerous one. The background to signal cross section ratio was estimated under different cut combinations of the particle identification information from the different detectors and of the kinematic fits. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.

Measurement of the forward-backward asymmetry of Z boson decays in electron-positron pairs with the ATLAS detector in proton-proton collisions at root out s = 7TeV at the LHC

In this thesis the measurement of the effective weak mixing angle wma in proton-proton collisions is described. The results are extracted from the forward-backward asymmetry (AFB) in electron-positron final states at the ATLAS experiment at the LHC. The AFB is defined upon the distribution of the polar angle between the incoming quark and outgoing lepton. The signal process used in this study is the reaction pp to zgamma + X to ee + X taking a total integrated luminosity of 4.8\,fb^(-1) of data into account. The data was recorded at a proton-proton center-of-mass energy of sqrt(s)=7TeV. The weak mixing angle is a central parameter of the electroweak theory of the Standard Model (SM) and relates the neutral current interactions of electromagnetism and weak force. The higher order corrections on wma are related to other SM parameters like the mass of the Higgs boson.rnrnBecause of the symmetric initial state constellation of colliding protons, there is no favoured forward or backward direction in the experimental setup. The reference axis used in the definition of the polar angle is therefore chosen with respect to the longitudinal boost of the electron-positron final state. This leads to events with low absolute rapidity have a higher chance of being assigned to the opposite direction of the reference axis. This effect called dilution is reduced when events at higher rapidities are used. It can be studied including electrons and positrons in the forward regions of the ATLAS calorimeters. Electrons and positrons are further referred to as electrons. To include the electrons from the forward region, the energy calibration for the forward calorimeters had to be redone. This calibration is performed by inter-calibrating the forward electron energy scale using pairs of a central and a forward electron and the previously derived central electron energy calibration. The uncertainty is shown to be dominated by the systematic variations.rnrnThe extraction of wma is performed using chi^2 tests, comparing the measured distribution of AFB in data to a set of template distributions with varied values of wma. The templates are built in a forward folding technique using modified generator level samples and the official fully simulated signal sample with full detector simulation and particle reconstruction and identification. The analysis is performed in two different channels: pairs of central electrons or one central and one forward electron. The results of the two channels are in good agreement and are the first measurements of wma at the Z resonance using electron final states at proton-proton collisions at sqrt(s)=7TeV. The precision of the measurement is already systematically limited mostly by the uncertainties resulting from the knowledge of the parton distribution functions (PDF) and the systematic uncertainties of the energy calibration.rnrnThe extracted results of wma are combined and yield a value of wma_comb = 0.2288 +- 0.0004 (stat.) +- 0.0009 (syst.) = 0.2288 +- 0.0010 (tot.). The measurements are compared to the results of previous measurements at the Z boson resonance. The deviation with respect to the combined result provided by the LEP and SLC experiments is up to 2.7 standard deviations.

Geochronological and structural evolution of the western and central Kaoko Belt in NW Namibia

This thesis focusses on the tectonic evolution and geochronology of part of the Kaoko orogen, which is part of a network of Pan-African orogenic belts in NW Namibia. By combining geochemical, isotopic and structural analysis, the aim was to gain more information about how and when the Kaoko Belt formed. The first chapter gives a general overview of the studied area and the second one describes the basis of the Electron Probe Microanalysis dating method. The reworking of Palaeo- to Mesoproterozoic basement during the Pan-African orogeny as part of the assembly of West Gondwana is discussed in Chapter 3. In the study area, high-grade rocks occupy a large area, and the belt is marked by several large-scale structural discontinuities. The two major discontinuities, the Sesfontein Thrust (ST) and the Puros Shear Zone (PSZ), subdivide the orogen into three tectonic units: the Eastern Kaoko Zone (EKZ), the Central Kaoko Zone (CKZ) and the Western Kaoko Zone (WKZ). An important lineament, the Village Mylonite Zone (VMZ), has been identified in the WKZ. Since plutonic rocks play an important role in understanding the evolution of a mountain belt, zircons from granitoid gneisses were dated by conventional U-Pb, SHRIMP and Pb-Pb techniques to identify different age provinces. Four different age provinces were recognized within the Central and Western part of the belt, which occur in different structural positions. The VMZ seems to mark the limit between Pan-African granitic rocks east of the lineament and Palaeo- to Mesoproterozoic basement to the west. In Chapter 4 the tectonic processes are discussed that led to the Neoproterozoic architecture of the orogen. The data suggest that the Kaoko Belt experienced three main phases of deformation, D1-D3, during the Pan-African orogeny. Early structures in the central part of the study area indicate that the initial stage of collision was governed by underthrusting of the medium-grade Central Kaoko zone below the high-grade Western Kaoko zone, resulting in the development of an inverted metamorphic gradient. The early structures were overprinted by a second phase D2, which was associated with the development of the PSZ and extensive partial melting and intrusion of ~550 Ma granitic bodies in the high-grade WKZ. Transcurrent deformation continued during cooling of the entire belt, giving rise to the localized low-temperature VMZ that separates a segment of elevated Mesoproterozoic basement from the rest of the Western zone in which only Pan-African ages have so far been observed. The data suggest that the boundary between the Western and Central Kaoko zones represents a modified thrust zone, controlling the tectonic evolution of the Kaoko belt. The geodynamic evolution and the processes that generated this belt system are discussed in Chapter 5. Nd mean crustal residence ages of granitoid rocks permit subdivision of the belt into four provinces. Province I is characterised by mean crustal residence ages <1.7 Ga and is restricted to the Neoproterozoic granitoids. A wide range of initial Sr isotopic values (87Sr/86Sri = 0.7075 to 0.7225) suggests heterogeneous sources for these granitoids. The second province consists of Mesoproterozoic (1516-1448 Ma) and late Palaeo-proterozoic (1776-1701 Ma) rocks and is probably related to the Eburnian cycle with Nd model ages of 1.8-2.2 Ga. The eNd i values of these granitoids are around zero and suggest a predominantly juvenile source. Late Archaean and middle Palaeoproterozoic rocks with model ages of 2.5 to 2.8 Ga make up Province III in the central part of the belt and are distinct from two early Proterozoic samples taken near the PSZ which show even older TDM ages of ~3.3 Ga (Province IV). There is no clear geological evidence for the involvement of oceanic lithosphere in the formation of the Kaoko-Dom Feliciano orogen. Chapter 6 presents the results of isotopic analyses of garnet porphyroblasts from high-grade meta-igneous and metasedimentary rocks of the sillimanite-K-feldspar zone. Minimum P-T conditions for peak metamorphism were calculated at 731±10 °C at 6.7±1.2 kbar, substantially lower than those previously reported. A Sm-Nd garnet-whole rock errorchron obtained on a single meta-igneous rock yielded an unexpectedly old age of 692±13 Ma, which is interpreted as an inherited metamorphic age reflecting an early Pan-African granulite-facies event. The dated garnets survived a younger high-grade metamorphism that occurred between ca. 570 and 520 Ma and apparently maintained their old Sm-Nd isotopic systematics, implying that the closure temperature for garnet in this sample was higher than 730 °C. The metamorphic peak of the younger event was dated by electronmicroprobe on monazite at 567±5 Ma. From a regional viewpoint, it is possible that these granulites of igneous origin may be unrelated to the early Pan-African metamorphic evolution of the Kaoko Belt and may represent a previously unrecognised exotic terrane.

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

Construction and commissioning of a collinear laser spectroscopy setup at TRIGA Mainz and laser spectroscopy of magnesium isotopes at ISOLDE (CERN)

Collinear laser spectroscopy has been used as a tool for nuclear physics for more than 30 years. The unique possibility to extract nuclear properties like spins, radii and nuclear moments in a model-independent manner leads to important physics results to test the predictive power of existing nuclear models. rnThis work presents the construction and the commissioning of a new collinear laser spectroscopy experiment TRIGA-LASER as a part of the TRIGA-SPEC facility at the TRIGA research reactor at the University of Mainz. The goal of the experiment is to study the nuclear structure of radioactive isotopes which will be produced by neutron-induced fission near the reactor core and transported to an ion source by a gas jet system. rnThe versatility of the collinear laser spectroscopy technique will be exploited in the second part of this thesis. The nuclear spin and the magnetic moment of the neutron-deficient isotope Mg-21 will be presented, which were measured by the detection of the beta-decay asymmetry induced by nuclear polarization after optical pumping. A combination of this detection method with the classical fluorescence detection is then used to determine the isotope shifts of the neutron-rich magnesium isotopes from Mg-24 through Mg-32 to study the transition to the ''island of inversion''.

Detection of individual spin transitions of a single proton confined in a cryogenic Penning trap

Das in dieser Arbeit vorgestellte Experiment zur Messung des magnetischen Moments des Protons basiert auf der Messung des Verhältnisses von Zyklotronfrequenz und Larmorfrequenz eines einzelnen, in einer kryogenen Doppel-Penning Falle gespeicherten Protons. In dieser Arbeit konnten erstmalig zwei der drei Bewegungsfrequenzen des Protons gleichzeitig im thermischen Gleichgewicht mit entsprechenden hochsensitiven Nachweissystemen nicht-destruktiv detektiert werden, wodurch die Messzeit zur Bestimmung der Zyklotronfrequenz halbiert werden konnte. Ferner wurden im Rahmen dieser Arbeit erstmalig einzelne Spin-Übergänge eines einzelnen Protons detektiert, wodurch die Bestimmung der Larmorfrequenz ermöglicht wird. Mithilfe des kontinuierlichen Stern-Gerlach Effekts wird durch eine sogenannte magnetische Flasche das magnetische Moment an die axiale Bewegungsmode des Protons gekoppelt. Eine Änderung des Spinzustands verursacht folglich einen Frequenzsprung der axialen Bewegungsfrequenz, welche nicht-destruktiv gemessen werden kann. Erschwert wird die Detektion des Spinzustands dadurch, dass die axiale Frequenz nicht nur vom Spinmoment, sondern auch vom Bahnmoment abhängt. Die große experimentelle Herausforderung besteht also in der Verhinderung von Energieschwankungen in den radialen Bewegungsmoden, um die Detektierbarkeit von Spin-Übergängen zu gewährleisten. Durch systematische Studien zur Stabilität der axialen Frequenz sowie einer kompletten Überarbeitung des experimentellen Aufbaus, konnte dieses Ziel erreicht werden. Erstmalig kann der Spinzustand eines einzelnen Protons mit hoher Zuverlässigkeit bestimmt werden. Somit stellt diese Arbeit einen entscheidenden Schritt auf dem Weg zu einer hochpräzisen Messung des magnetischen Moments des Protons dar.