Imaging spin-filter efficiency of W(001) and Ir(001) single crystals

Während der letzten Jahre wurde für Spinfilter-Detektoren ein wesentlicher Schritt in Richtung stark erhöhter Effizienz vollzogen. Das ist eine wichtige Voraussetzung für spinaufgelöste Messungen mit Hilfe von modernen Elektronensp ektrometern und Impulsmikroskopen. In dieser Doktorarbeit wurden bisherige Arbeiten der parallel abbildenden Technik weiterentwickelt, die darauf beruht, dass ein elektronenoptisches Bild unter Ausnutzung der k-parallel Erhaltung in der Niedrigenergie-Elektronenbeugung auch nach einer Reflektion an einer kristallinen Oberfläche erhalten bleibt. Frühere Messungen basierend auf der spekularen Reflexion an einerrnW(001) Oberfläche [Kolbe et al., 2011; Tusche et al., 2011] wurden auf einenrnviel größeren Parameterbereich erweitert und mit Ir(001) wurde ein neues System untersucht, welches eine sehr viel längere Lebensdauer der gereinigten Kristalloberfläche im UHV aufweist. Die Streuenergie- und Einfallswinkel-“Landschaft” der Spinempfindlichkeit S und der Reflektivität I/I0 von gestreuten Elektronen wurde im Bereich von 13.7 - 36.7 eV Streuenergie und 30◦ - 60◦ Streuwinkel gemessen. Die dazu neu aufgebaute Messanordnung umfasst eine spinpolarisierte GaAs Elektronenquellernund einen drehbaren Elektronendetektor (Delayline Detektor) zur ortsauflösenden Detektion der gestreuten Elektronen. Die Ergebnisse zeigen mehrere Regionen mit hoher Asymmetrie und großem Gütefaktor (figure of merit FoM), definiert als S2 · I/I0. Diese Regionen eröffnen einen Weg für eine deutliche Verbesserung der Vielkanal-Spinfiltertechnik für die Elektronenspektroskopie und Impulsmikroskopie. Im praktischen Einsatz erwies sich die Ir(001)-Einkristalloberfläche in Bezug auf längere Lebensdauer im UHV (ca. 1 Messtag), verbunden mit hoher FOM als sehr vielversprechend. Der Ir(001)-Detektor wurde in Verbindung mit einem Halbkugelanalysator bei einem zeitaufgelösten Experiment im Femtosekunden-Bereich am Freie-Elektronen-Laser FLASH bei DESY eingesetzt. Als gute Arbeitspunkte erwiesen sich 45◦ Streuwinkel und 39 eV Streuenergie, mit einer nutzbaren Energiebreite von 5 eV, sowie 10 eV Streuenergie mit einem schmaleren Profil von < 1 eV aber etwa 10× größerer Gütefunktion. Die Spinasymmetrie erreicht Werte bis 70 %, was den Einfluss von apparativen Asymmetrien deutlich reduziert. Die resultierende Messungen und Energie-Winkel-Landschaft zeigt recht gute Übereinstimmung mit der Theorie (relativistic layer-KKR SPLEED code [Braun et al., 2013; Feder et al.,rn2012])

Liquid crystalline oligofluorenes and their derivatives

Homo-oligofluorenes (OFn), polyfluorenes (PF2/6) and oligofluorenes with one fluorenenone group in the center (OFnK) were synthesized. They were used as model compounds to understand of the structure-property relationships of polyfluorenes and the origin of the green emission in the photoluminescence (after photooxidation of the PFs) and the electroluminescence (EL) spectra. The electronic, electrochemical properties, thermal behavior, supramolecular self-assembly, and photophysical properties of OFn, PF2/6 and OFnK were investigated. Oligofluorenes with 2-ethylhexyl side chain (OF2-OF7) from the dimer up to the heptamer were prepared by a series of stepwise transition metal mediated Suzuki and Yamamoto coupling reactions. Polyfluorene was synthesized by Yamamoto coupling of 2,7-dibromo-9,9-bis(2-ethylhexyl)fluorene. Oligofluorenes with one fluorenone group in the center (OF3K, OF5K, OF7K) were prepared by Suzuki coupling between the monoboronic fluorenyl monomer, dimer, trimer and 2, 7-dibromofluorenone. The electrochemical and electronic properties of homo-oligofluorenes (OFn) were systematically studied by several combined techniques such as cyclic voltammetry, differential pulse voltammetry, UV-vis absorption spectroscopy, steady and time-resolved fluorescence spectroscopy. It was found that the oligofluorenes behave like classical conjugated oligomers, i.e., with the increase of the chain-length, the corresponding oxidation potential, the absorption and emission maximum, ionization potential, electron affinity, band gap and the photoluminescence lifetime displayed a very good linear relation with the reciprocal number of the fluorene units (1/n). The extrapolation of these linear relations to infinite chain length predicted the electrochemical and electronic properties of the corresponding polyfluorenes. The thermal behavior, single-crystal structure and supramolecular packing, alignment properties, and molecular dynamics of the homo-oligofluorenes (OFn) up to the polymer were studied using techniques such as TGA, DSC, WAXS, POM and DS. The OFn from tetramer to heptamer show a smectic liquid crystalline phase with clearly defined isotropization temperature. The oligomers do show a glass transition which exhibits n-1 dependence and allows extrapolation to a hypothetical glass transition of the polymer at around 64 °C. A smectic packing and helix-like conformation for the oligofluorenes from tetramer to heptamer was supported by WAXS experiments, simulation, and single-crystal structure of some oligofluorene derivatives. Oligofluorenes were aligned more easily than the corresponding polymer, and the alignability increased with the molecular length from tetramer to heptamer. The molecular dynamics in a series of oligofluorenes up to the polymer was studied using dielectric spectroscopy. The photophysical properties of OFn and PF2/6 were investigated by the steady-state spectra (UV-vis absorption and fluorescence spectra) and time-resolved fluorescence spectra both in solution and thin film. The time-resolved fluorescence spectra of the oligofluorenes were measured by streak camera and gate detection technique. The lifetime of the oligofluorenes decreased with the extension of the chain-length. No green emission was observed in CW, prompt and delayed fluorescence for oligofluorenes in m-THF and film at RT and 77K. Phosphorescence was observed for oligofluorenes in frozen dilute m-THF solution at 77K and its lifetime increased with length of oligofluorenes. A linear relation was obtained for triplet energy and singlet energy as a function of the reciprocal degree of polymerization, and the singlet-triplet energy gap (S1-T1) was found to decrease with the increase of degree of polymerization. Oligofluorenes with one fluorenone unit at the center were used as model compounds to understand the origin of the low-energy (“green”) emission band in the photoluminescence and electroluminescence spectra of polyfluorenes. Their electrochemical properties were investigated by CV, and the ionization potential (Ip) and electron affinity (Ea) were calculated from the onset of oxidation and reduction of OFnK. The photophysical properties of OFnK were studied in dilute solution and thin film by steady-state spectra and time-resolved fluorescence spectra. A strong green emission accompanied with a weak blue emission were obtained in solution and only green emission was observed on film. The strong green emission of OFnK suggested that rapid energy transfer takes place from higher energy sites (fluorene segments) to lower energy sites (fluorenone unit) prior to the radiative decay of the excited species. The fluorescence spectra of OFnK also showed solvatochromism. Monoexponential decay behaviour was observed by time-resolved fluorescence measurements. In addition, the site-selective excitation and concentration dependence of the fluorescence spectra were investigated. The ratio of green and blue emission band intensities increases with the increase of the concentration. The observed strong concentration dependence of the green emission band in solution suggests that increased interchain interactions among the fluorenone-containing oligofluorene chain enhanced the emission from the fluorenone defects at higher concentration. On the other hand, the mono-exponential decay behaviour and power dependence were not influenced significantly by the concentration. We have ruled out the possibility that the green emission band originates from aggregates or excimer formation. Energy transfer was further investigated using a model system of a polyfluorene doped by OFnK. Förster-type energy transfer took place from PF2/6 to OFnK, and the energy transfer efficiency increased with increasing of the concentration of OFnK. Efficient funneling of excitation energy from the high-energy fluorene segments to the low-energy fluorenone defects results from energy migration by hopping of excitations along a single polymer chain until they are trapped on the fluorenone defects on that chain or transferred onto neighbouring chains by Förster-type interchain energy transfer process. These results imply that the red-shifted emission in polyfluorenes can originate from (usually undesirable) keto groups at the bridging carbon atoms-especially if the samples have been subject to photo- or electro-oxidation or if fluorenone units are present due to an improper purification of the monomers prior to polymerization.

Electronic energy transfer processes in pi-conjugated polymers

Currently pi-conjugated polymers are considered as technologically interesting materials to be used as functional building elements for the development of the new generation of optoelectronic devices. More specifically during the last few years, poly-p-phenylene materials have attracted considerable attention for their blue photoluminescence properties. This Thesis deals with the optical properties of the most representative blue light poly-p-phenylene emitters such as poly(fluorene), oligo(fluorene), poly(indenofluorene) and ladder-type penta(phenylene) derivatives. In the present work, laser induced photoluminescence spectroscopy is used as a major tool for the study of the interdependence between the dynamics of the probed photoluminescence, the molecular structures of the prepared polymeric films and the presence of chemical defects. Complementary results obtained by two-dimensional wide-angle X-ray diffraction are reported. These findings show that the different optical properties observed are influenced by the intermolecular solid-state interactions that in turn are controlled by the pendant groups of the polymer backbone. A significant feedback is delivered regarding the positive impact of a new synthetic route for the preparation of a poly(indenofluorene) derivative on the spectral purity of the compound. The energy transfer mechanisms that operate in the studied systems are addressed by doping experiments. After the evaluation of the structure/property interdependence, a new optical excitation pathway is presented. An efficient photon low-energy up-conversion that sensitises the blue emission of poly(fluorene) is demonstrated. The observed phenomenon takes place in poly(fluorene) derivatives hosts doped with metallated octaethyl porphyrins, after quasi-CW photoexcitation of intensities in the order of kW/cm2. The up-conversion process is parameterised in terms of temperature, wavelength excitation and central metal cation in the porphyrin ring. Additionally the observation of the up-conversion is extended in a broad range of poly-p-phenylene blue light emitting hosts. The dependence of the detected up-conversion intensity on the excitation intensity and doping concentration is reported. Furthermore the dynamics of the up-conversion intensity are monitored as a function of the doping concentration. These experimental results strongly suggest the existence of triplet-triplet annihilation events into the porphyrin molecules that are subsequently followed by energy transfer to the host. After confirming the occurrence of the up-conversion in solutions, cyclic voltammetry is used in order to show that the up-conversion efficiency is partially determined from the energetic alignment between the HOMO levels of the host and the dopant.

QCD-Strahlungskorrekturen zu Polarisationsobservablen in semileptonischen Zerfällen schwerer Quarks

In dieser Arbeit werden die QCD-Strahlungskorrekturen in erster Ordnung der starken Kopplungskonstanten für verschiedene Polarisationsobservablen zu semileptonischen Zerfällen eines bottom-Quarks in ein charm-Quark und ein Leptonpaar berechnet. Im ersten Teil wird der Zerfall eines unpolarisierten b-Quarks in ein polarisiertes c-Quark sowie ein geladenes Lepton und ein Antineutrino im Ruhesystem des b-Quarks analysiert. Es werden die Strahlungskorrekturen für den unpolarisierten und den polarisierten Beitrag zur differentiellen Zerfallsrate nach der Energie des c-Quarks berechnet, wobei das geladene Lepton als leicht angesehen und seine Masse daher vernachlässigt wird. Die inklusive differentielle Rate wird durch zwei Strukturfunktionen in analytischer Form dargestellt. Anschließend werden die Strukturfunktionen und die Polarisation des c-Quarks numerisch ausgewertet. Nach der Einführung der Helizitäts-Projektoren befaßt sich der zweite Teil mit dem kaskadenartigen Zerfall eines polarisierten b-Quarks in ein unpolarisiertes c-Quark und ein virtuelles W-Boson, welches weiter in ein Paar leichter Leptonen zerfällt. Es werden die inklusiven Strahlungskorrekturen zu drei unpolarisierten und fünf polarisierten Helizitäts-Strukturfunktionen in analytischer Form berechnet, welche die Winkelverteilung für die differentielle Zerfallsrate nach dem Viererimpulsquadrat des W-Bosons beschreiben. Die Strukturfunktionen enthalten die Informationen sowohl über die polare Winkelverteilung zwischen dem Spinvektor des b-Quarks und dem Impulsvektor des W-Bosons als auch über die räumliche Winkelverteilung zwischen den Impulsen des W-Bosons und des Leptonpaars. Der Impuls und der Spinvektor des b-Quarks sowie der Impuls des W-Bosons werden im b-Ruhesystem analysiert, während die Impulse des Leptonpaars im W-Ruhesystem ausgewertet werden. Zusätzlich zu den genannten Strukturfunktionen werden noch die unpolarisierte und die polarisierte skalare Strukturfunktion angegeben, die in Anwendungen bei hadronischen Zerfällen eine Rolle spielen. Anschließend folgt eine numerische Auswertung aller berechneten Strukturfunktionen. Im dritten Teil werden die nichtperturbativen HQET-Korrekturen zu inklusiven semileptonischen Zerfällen schwerer Hadronen diskutiert, welche ein b-Quark enthalten. Sie beschreiben hadronische Korrekturen, die durch die feste Bindung des b-Quarks in Hadronen hervorgerufen werden. Es werden insgesamt fünf unpolarisierte und neun polarisierte Helizitäts-Strukturfunktionen in analytischer Form angegeben, die auch eine endliche Masse und den Spin des geladenen Leptons berücksichtigen. Die Strukturfunktionen werden sowohl in differentieller Form in Abhängigkeit des quadrierten Viererimpulses des W-Bosons als auch in integrierter Form präsentiert. Zum Schluß werden die zuvor erhaltenen Resultate auf die semi-inklusiven hadronischen Zerfälle eines polarisierten Lambda_b-Baryons oder eines B-Mesons in ein D_s- oder ein D_s^*-Meson unter Berücksichtigung der D_s^*-Polarisation angewandt. Für die zugehörigen Winkelverteilungen werden die inklusiven QCD- und die nichtperturbativen HQET-Korrekturen zu den Helizitäts-Strukturfunktionen in analytischer Form angegeben und anschließend numerisch ausgewertet.

Quantum gravity effects in rotating black hole spacetimes

The aim of this work is to explore, within the framework of the presumably asymptotically safe Quantum Einstein Gravity, quantum corrections to black hole spacetimes, in particular in the case of rotating black holes. We have analysed this problem by exploiting the scale dependent Newton s constant implied by the renormalization group equation for the effective average action, and introducing an appropriate "cutoff identification" which relates the renormalization scale to the geometry of the spacetime manifold. We used these two ingredients in order to "renormalization group improve" the classical Kerr metric that describes the spacetime generated by a rotating black hole. We have focused our investigation on four basic subjects of black hole physics. The main results related to these topics can be summarized as follows. Concerning the critical surfaces, i.e. horizons and static limit surfaces, the improvement leads to a smooth deformation of the classical critical surfaces. Their number remains unchanged. In relation to the Penrose process for energy extraction from black holes, we have found that there exists a non-trivial correlation between regions of negative energy states in the phase space of rotating test particles and configurations of critical surfaces of the black hole. As for the vacuum energy-momentum tensor and the energy conditions we have shown that no model with "normal" matter, in the sense of matter fulfilling the usual energy conditions, can simulate the quantum fluctuations described by the improved Kerr spacetime that we have derived. Finally, in the context of black hole thermodynamics, we have performed calculations of the mass and angular momentum of the improved Kerr black hole, applying the standard Komar integrals. The results reflect the antiscreening character of the quantum fluctuations of the gravitational field. Furthermore we calculated approximations to the entropy and the temperature of the improved Kerr black hole to leading order in the angular momentum. More generally we have proven that the temperature can no longer be proportional to the surface gravity if an entropy-like state function is to exist.

The C-4-Dicarboxylate carriers DcuB and DctA of Escherichia coli: function as cosensors and topology

Das fakultativ anaerobe Enterobakterium Escherichia coli nutzt C4-Dicarboxylate sowohl unter aeroben als auch anaeroben Bedingungen als Kohlenstoff- und Energiequelle. Die Aufnahme der C4-Dicarboxylaten und die Energiekonservierung mittels Fumaratatmung wird durch das Zweikomponentensystem DcuSR reguliert. Die Sensorhistidinkinase DcuS und der nachgeschaltete Responseregulator DcuR aktivieren bei Verfügbarkeit von C4-Dicarboxylaten die Expression der Gene für den Succinat Transporter DctA, den anaeroben Fumarat/Succinat Antiporter DcuB, die Fumarase B sowie die Fumaratreduktase FrdABCD. Die Transportproteine DctA und DcuB wiederum regulieren die Expression der DcuSR-abhängigen Gene negativ. Fehlen von DctA oder DcuB resultiert bereits ohne Effektor in einer maximalen Expression von dctA bzw. dcuB. Durch gerichtete und ungerichtete Mutagenese wurde gezeigt, dass die Transportfunktion des Carriers DcuB unabhängig von seiner regulatorischen Funktion ist. DcuB kann daher als Cosensor des DcuSR Systems angesehen werden.rnUnter Verwendung von Reportergenfusionen von C-terminal verkürzten Konstrukten von DcuB mit der Alkalischen Phosphatase und der β-Galactosidase wurde die Topologie des Multitransmembranproteins DcuB bestimmt. Zusätzlich wurde die Zugänglichkeit bestimmter Aminosäurereste durch chemische Modifikation mit membran-durchlässigen und membran-undurchlässigen Thiolreagenzien untersucht. Die erhaltenen Ergebnisse deuten auf die Existenz eines tief in die Membran reichenden, hydrophilen Kanal hin, welcher zum Periplasma hin geöffnet ist. Mit Hilfe der Topologie-Studien, des Hydropathie-Blots und der Sekundärstruktur-Vorhersage wurde ein Modell des Carriers erstellt. DcuB besitzt kurze, periplasmatisch liegende Proteinenden, die durch 12 Transmembranhelices und zwei große hydrophile Schleifen jeweils zwischen TM VII/VIII und TM XI/XII verbunden sind. Die regulatorisch relevanten Reste K353, T396 und D398 befinden sich innerhalb von TM XI sowie auf der angrenzenden cytoplasmatischen Schleife XI-XII. Unter Berücksichtigung der strukturellen und funktionellen Aspekte wurde ein Regulationsmodell erstellt, welches die gemeinsam durch DcuB und DcuS kontrollierte C4-Dicarboxylat-abhängige Genexpression darstellt. rnDer Effekt von DctA und DcuSR auf die Expression einer dctA´-´lacZ Reportergenfusion und auf die aerobe C4-Dicarboxylat-Aufnahme wurde untersucht. In-vivo FRET-Messungen weisen auf eine direkte Wechselwirkung zwischen dem Carrier DctA und dem Sensor DcuS hin. Dieses Ergebnis stützt die Theorie der Regulation von DcuS durch C4-Dicarboxylate und durch die Cosensoren DctA bzw. DcuB mittels direkter Protein-Protein Interaktion.rn

Quantum dot-dye hybrid systems for energy transfer applications

In this thesis, we focus on the preparation of energy transfer-based quantum dot (QD)-dye hybrid systems. Two kinds of QD-dye hybrid systems have been successfully synthesized: QD-silica-dye and QD-dye hybrid systems.rn rnIn the QD-silica-dye hybrid system, multishell CdSe/CdS/ZnS QDs were adsorbed onto monodisperse Stöber silica particles with an outer silica shell of thickness 2 - 24 nm containing organic dye molecules (Texas Red). The thickness of this dye layer has a strong effect on the total sensitized acceptor emission, which is explained by the increase in the number of dye molecules homogeneously distributed within the silica shell, in combination with an enhanced surface adsorption of QDs with increasing dye amount. Our conclusions were underlined by comparison of the experimental results with Monte-Carlo simulations, and by control experiments confirming attractive interactions between QDs and Texas Red freely dissolved in solution. rnrnNew QD-dye hybrid system consisting of multishell QDs and organic perylene dyes have been synthesized. We developed a versatile approach to assemble extraordinarily stable QD-dye hybrids, which uses dicarboxylate anchors to bind rylene dyes to QD. This system yields a good basis to study the energy transfer between QD and dye because of its simple and compact design: there is no third kind of molecule linking QD and dye; no spacer; and the affinity of the functional group to the QD surface is strong. The FRET signal was measured for these complexes as a function of both dye to QD ratio and center-to-center distance between QD and dye by controlling number of covered ZnS layers. Data showed that fluorescence resonance energy transfer (FRET) was the dominant mechanism of the energy transfer in our QD-dye hybrid system. FRET efficiency can be controlled by not only adjusting the number of dyes on the QD surface or the QD to dye distance, but also properly choosing different dye and QD components. Due to the strong stability, our QD-dye complexes can also be easily transferred into water. Our approach can apply to not only dye molecules but also other organic molecules. As an example, the QDs have been complexed with calixarene molecules and the QD-calixarene complexes also have potential for QD-based energy transfer study. rn

The electron antineutrino angular correlation coefficient a in free neutron decay: Testing the standard model with the aSPECT-spectrometer

The beta-decay of free neutrons is a strongly over-determined process in the Standard Model (SM) of Particle Physics and is described by a multitude of observables. Some of those observables are sensitive to physics beyond the SM. For example, the correlation coefficients of the involved particles belong to them. The spectrometer aSPECT was designed to measure precisely the shape of the proton energy spectrum and to extract from it the electron anti-neutrino angular correlation coefficient "a". A first test period (2005/ 2006) showed the “proof-of-principles”. The limiting influence of uncontrollable background conditions in the spectrometer made it impossible to extract a reliable value for the coefficient "a" (publication: Baessler et al., 2008, Europhys. Journ. A, 38, p.17-26). A second measurement cycle (2007/ 2008) aimed to under-run the relative accuracy of previous experiments (Stratowa et al. (1978), Byrne et al. (2002)) da/a =5%. I performed the analysis of the data taken there which is the emphasis of this doctoral thesis. A central point are background studies. The systematic impact of background on a was reduced to da/a(syst.)=0.61 %. The statistical accuracy of the analyzed measurements is da/a(stat.)=1.4 %. Besides, saturation effects of the detector electronics were investigated which were initially observed. These turned out not to be correctable on a sufficient level. An applicable idea how to avoid the saturation effects will be discussed in the last chapter.

Stacked searches for high-energy neutrinos from blazars with IceCube

In the year 2013, the detection of a diffuse astrophysical neutrino flux with the IceCube neutrino telescope – constructed at the geographic South Pole – was announced by the IceCube collaboration. However, the origin of these neutrinos is still unknown as no sources have been identified to this day. Promising neutrino source candidates are blazars, which are a subclass of active galactic nuclei with radio jets pointing towards the Earth. In this thesis, the neutrino flux from blazars is tested with a maximum likelihood stacking approach, analyzing the combined emission from uniform groups of objects. The stacking enhances the sensitivity w.r.t. the still unsuccessful single source searches. The analysis utilizes four years of IceCube data including one year from the completed detector. As all results presented in this work are compatible with background, upper limits on the neutrino flux are given. It is shown that, under certain conditions, some hadronic blazar models can be challenged or even rejected. Moreover, the sensitivity of this analysis – and any other future IceCube point source search – was enhanced by the development of a new angular reconstruction method. It is based on a detailed simulation of the photon propagation in the Antarctic ice. The median resolution for muon tracks, induced by high-energy neutrinos, is improved for all neutrino energies above IceCube’s lower threshold at 0.1TeV. By reprocessing the detector data and simulation from the year 2010, it is shown that the new method improves IceCube’s discovery potential by 20% to 30% depending on the declination.

Single meson production in proton diffraction at 190 GeV/c at COMPASS

The quark model successfully describes all ground state bary-ons as members of $SU(N)$ flavour multiplets. For excited baryon states the situation is totally different. There are much less states found in the experiment than predicted in most theoretical calculations. This fact has been known for a long time as the 'missing resonance problem'. In addition, many states found in experiments are only poorly measured up to now. Therefore, further experimental efforts are needed to clarify the situation.rnrnAt mbox{COMPASS}, reactions of a $190uskgigaeVperclight$ hadron beam impinging on a liquid hydrogen target are investigated.rnThe hadron beam contains different species of particles ($pi$, $K$, $p$). To distinguish these particles, two Cherenkov detectors are used. In this thesis, a new method for the identification of particles from the detector information is developed. This method is based on statistical approaches and allows a better kaon identification efficiency with a similar purity compared to the method, which was used before.rnrnThe reaction $pprightarrow ppX$ with $X=(pi^0,~eta,~omega,~phi)$ is used to study different production mechanisms. A previous analysis of $omega$ and $phi$ mesons is extended to pseudoscalar mesons. As the resonance contributions in $peta$ are smaller than in $ppi^0$ a different behaviour of these two final states is expected as a function of kinematic variables. The investigation of these differences allows to study different production mechanisms and to estimate the size of the resonant contribution in the different channels.rnrnIn addition, the channel $pprightarrow ppX$ allows to study baryon resonances in the $pX$ system.rnIn the mbox{COMPASS} energy regime, the reaction is dominated by Pomeron exchange. As a Pomeron carries vacuum quantum numbers, no isospin is transferred between the target proton and the beam proton. Therefore, the $pX$ final state has isospin $textstylefrac{1}{2}$ and all baryon resonances in this channel are $N^ast$ baryons. This offers the opportunity to do spectroscopy without taking $Delta$ resonances into account. rnrnTo disentangle the contributions of different resonances a partial wave analysis (PWA) is used. Different resonances have different spin and parity $J^parity$, which results in different angular distributions of the decay particles. These angular distributions can be calculated from models and then be fitted to the data. From the fit the contributions of the single resonances as well as resonance parameters -- namely the mass and the width -- can be extracted. In this thesis, two different approaches for a partial wave analysis of the reaction $pprightarrow pppi^0$ are developed and tested.