Polarization observables in virtual compton scattering

Virtual Compton Scattering (VCS) is an important reaction for understanding nucleon structure at low energies. By studying this process, the generalized polarizabilities of the nucleon can be measured. These observables are a generalization of the already known polarizabilities and will permit theoretical models to be challenged on a new level. More specifically, there exist six generalized polarizabilities and in order to disentangle them all, a double polarization experiment must be performed. Within this work, the VCS reaction p(e,e p)gamma was measured at MAMI using the A1 Collaboration three spectrometer setup with Q2=0.33 (GeV/c)2. Using the highly polarized MAMI beam and a recoil proton polarimeter, it was possible to measure both the VCS cross section and the double polarization observables. Already in 2000, the unpolarized VCS cross section was measured at MAMI. In this new experiment, we could confirm the old data and furthermore the double polarization observables were measured for the first time. The data were taken in five periods between 2005 and 2006. In this work, the data were analyzed to extract the cross section and the proton polarization. For the analysis, a maximum likelihood algorithm was developed together with the full simulation of all the analysis steps. The experiment is limited by the low statistics due mainly to the focal plane proton polarimeter efficiency. To overcome this problem, a new determination and parameterization of the carbon analyzing power was performed. The main result of the experiment is the extraction of a new combination of the generalized polarizabilities using the double polarization observables.

Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

108 Sn studied with intermediate-energy Coulomb excitation

In dieser Arbeit wurde der instabile, Neutronenarme Kern 108Sn mit Hilfe der Coulomb-Anregung bei intermediaeren Energien in inverser Kinematik studiert. Diese Methode wurde bisher zur Untersuchung der ersten angeregten 2+ Zustaende und deren E2 Zerfallsraten in Kernen mit Kernladungszahl Z< 30 angewendet. 108Sn ist somit der Kern mit der groeßten Kernladungszahl, bei dem diese Studien bisher stattfanden. Das Ziel dieses Experiments war die Messung der unbekannten reduzierten Uebergangswahrscheinlichkeit B(E2,0+ -> 2+). Der B(E2)-Wert von 0.230(57) e2b2 wurde relativ zu dem bekannten Wert des Isotops 112Sn bestimmt. Das Experiment wurde an der GSI Darmstadt mit Hilfe des RISING Detektors und des Fragmentseperators (FRS) durchgefuehrt. Sekundaere Strahlen (108Sn, 112Sn) mit einer Energie von ca. 150 MeV pro Nukleon wurden auf ein 386 mg/cm2 dickes 197Au Target geschossen. Die Projektilfragmente wurden mit Hilfe des Fragmentseparators selektiert und identifiziert. Zur Selektion des Reaktionskanals und zur Bestimmung des Winkels der gestreuten Fragmente wurde das Teilchenteleskop CATE, das sich hinter dem Target befand, verwendet. Gammastrahlung, die in Koinzidenz mit den Projektilrestkernen emittiert wurde, wurde in den Germanium-Cluster Detektoren des RISING Detektors nachgewiesen. Der gemessene B(E2,0+ -> 2+)-Wert von 108Sn ist in Uebereinstimmung mit neueren Schalenmodellrechnungen, die auf realistischen effektiven Wechselwirkungen basieren und im Rahmen eines verallgemeinerten Seniorit¨ats-Schemas erklaert werden.

Polarization in heavy quark decays

In this thesis I concentrate on the angular correlations in top quark decays and their next--to--leading order (NLO) QCD corrections. I also discuss the leading--order (LO) angular correlations in unpolarized and polarized hyperon decays. In the first part of the thesis I calculate the angular correlation between the top quark spin and the momentum of decay products in the rest frame decay of a polarized top quark into a charged Higgs boson and a bottom quark in Two-Higgs-Doublet-Models: $t(uparrow)rightarrow b+H^{+}$. The decay rate in this process is split into an angular independent part (unpolarized) and an angular dependent part (polar correlation). I provide closed form formulae for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized and the polar correlation functions for $m_{b}neq 0$ and $m_{b}=0$. The results for the unpolarized rate agree with the existing results in the literature. The results for the polarized correlations are new. I found that, for certain values of $tanbeta$, the ${mathcal O}(alpha_s)$ radiative corrections to the unpolarized, polarized rates, and the asymmetry parameter can become quite large. In the second part I concentrate on the semileptonic rest frame decay of a polarized top quark into a bottom quark and a lepton pair: $t(uparrow) to X_b + ell^+ + nu_ell$. I analyze the angular correlations between the top quark spin and the momenta of the decay products in two different helicity coordinate systems: system 1a with the $z$--axis along the charged lepton momentum, and system 3a with the $z$--axis along the neutrino momentum. The decay rate then splits into an angular independent part (unpolarized), a polar angle dependent part (polar correlation) and an azimuthal angle dependent part (azimuthal correlation). I present closed form expressions for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized part and the polar and azimuthal correlations in system 1a and 3a for $m_{b}neq 0$ and $m_{b}=0$. For the unpolarized part and the polar correlation I agree with existing results. My results for the azimuthal correlations are new. In system 1a I found that the azimuthal correlation vanishes in the leading order as a consequence of the $(V-A)$ nature of the Standard Model current. The ${mathcal O}(alpha_{s})$ radiative corrections to the azimuthal correlation in system 1a are very small (around 0.24% relative to the unpolarized LO rate). In system 3a the azimuthal correlation does not vanish at LO. The ${mathcal O}(alpha_{s})$ radiative corrections decreases the LO azimuthal asymmetry by around 1%. In the last part I turn to the angular distribution in semileptonic hyperon decays. Using the helicity method I derive complete formulas for the leading order joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. This is demonstrated by the specific example of the polarized hyperon decay $Xi^0(uparrow) to Sigma^+ + l^- + bar{nu}_l$ ,($l^-=e^-, mu^-$) followed by the nonleptonic decay $Sigma^+ to p + pi^0$, which is described by a five--fold angular decay distribution.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Algebraische Zyklen auf abelschen Varietäten der Dimension 4 mit Polarisierung von Typ (1,2,2,2)

Diese Arbeit besch"aftigt sich mit algebraischen Zyklen auf komplexen abelschen Variet"aten der Dimension 4. Ziel der Arbeit ist ein nicht-triviales Element in $Griff^{3,2}(A^4)$ zu konstruieren. Hier bezeichnet $A^4$ die emph{generische} abelsche Variet"at der Dimension 4 mit Polarisierung von Typ $(1,2,2,2)$. Die ersten drei Kapitel sind eine Wiederholung von elementaren Definitionen und Begriffen und daher eine Festlegung der Notation. In diesen erinnern wir an elementare Eigenschaften der von Saito definierten Filtrierungen $F_S$ und $Z$ auf den Chowgruppen (vgl. cite{Sa0} und cite{Sa}). Wir wiederholen auch eine Beziehung zwischen der $F_S$-Filtrierung und der Zerlegung von Beauville der Chowgruppen (vgl. cite{Be2} und cite{DeMu}), welche aus cite{Mu} stammt. Die wichtigsten Begriffe in diesem Teil sind die emph{h"ohere Griffiths' Gruppen} und die emph{infinitesimalen Invarianten h"oherer Ordnung}. Dann besch"aftigen wir uns mit emph{verallgemeinerten Prym-Variet"aten} bez"uglich $(2:1)$ "Uberlagerungen von Kurven. Wir geben ihre Konstruktion und wichtige geometrische Eigenschaften und berechnen den Typ ihrer Polarisierung. Kapitel ref{p-moduli} enth"alt ein Resultat aus cite{BCV} "uber die Dominanz der Abbildung $p(3,2):mathcal R(3,2)longrightarrow mathcal A_4(1,2,2,2)$. Dieses Resultat ist von Relevanz f"ur uns, weil es besagt, dass die generische abelsche Variet"at der Dimension 4 mit Polarisierung von Typ $(1,2,2,2)$ eine verallgemeinerte Prym-Variet"at bez"uglich eine $(2:1)$ "Uberlagerung einer Kurve vom Geschlecht $7$ "uber eine Kurve vom Geschlecht $3$ ist. Der zweite Teil der Dissertation ist die eigentliche Arbeit und ist auf folgende Weise strukturiert: Kapitel ref{Deg} enth"alt die Konstruktion der Degeneration von $A^4$. Das bedeutet, dass wir in diesem Kapitel eine Familie $Xlongrightarrow S$ von verallgemeinerten Prym-Variet"aten konstruieren, sodass die klassifizierende Abbildung $Slongrightarrow mathcal A_4(1,2,2,2)$ dominant ist. Desweiteren wird ein relativer Zykel $Y/S$ auf $X/S$ konstruiert zusammen mit einer Untervariet"at $Tsubset S$, sodass wir eine explizite Beschreibung der Einbettung $Yvert _Thookrightarrow Xvert _T$ angeben k"onnen. Das letzte und wichtigste Kapitel enth"ahlt Folgendes: Wir beweisen dass, die emph{ infinitesimale Invariante zweiter Ordnung} $delta _2(alpha)$ von $alpha$ nicht trivial ist. Hier bezeichnet $alpha$ die Komponente von $Y$ in $Ch^3_{(2)}(X/S)$ unter der Beauville-Zerlegung. Damit und mit Hilfe der Ergebnissen aus Kapitel ref{Cohm} k"onnen wir zeigen, dass [ 0neq [alpha ] in Griff ^{3,2}(X/S) . ] Wir k"onnen diese Aussage verfeinern und zeigen (vgl. Theorem ref{a4}) begin{theorem}label{maintheorem} F"ur $sin S$ generisch gilt [ 0neq [alpha _s ]in Griff ^{3,2}(A^4) , ] wobei $A^4$ die generische abelsche Variet"at der Dimension $4$ mit Polarisierung vom Typ $(1,2,2,2)$ ist. end{theorem}

Sensitivity enhancement in NMR by using parahydrogen induced polarization

Enhancing the sensitivity of nuclear magnetic resonance measurements via hyperpolarization techniques like parahydrogen induced polarization (PHIP) is of high interest for spectroscopic investigations. Parahydrogen induced polarization is a chemical method, which makes use of the correlation between nuclear spins in parahydrogen to create hyperpolarized molecules. The key feature of this technique is the pairwise and simultaneous transfer of the two hydrogen atoms of parahydrogen to a double or triple bond resulting in a population of the Zeeman energy levels different from the Boltzmann equation. The obtained hyperpolarization results in antiphase peaks in the NMR spectrum with high intensities. Due to these strong NMR signals, this method finds arnlot of applications in chemistry e.g. the characterization of short-lived reaction intermediates. Also in medicine it opens up the possibility to boost the sensitivity of medical diagnostics via magnetic labeling of active contrast agents. Thus, further examination and optimization of the PHIP technique is of significant importance in order to achieve the highest possible sensitivity gain.rnrnIn this work, different aspects concerning PHIP were studied with respect to its chemical and spectroscopic background. The first part of this work mainly focused on optimizing the PHIP technique by investigating different catalyst systems and developing new setups for the parahydrogenation. Further examinations facilitated the transfer of the generated polarization from the protons to heteronuclei like 13C. The second part of this thesis examined the possibility to transfer these results to different biologically active compounds to enable their later application in medical diagnostics. Onerngroup of interesting substances is represented by metabolites or neurotransmitters in mammalian cells. Other interesting substances are clinically relevant drugs like a barbituric acid derivative or antidepressant drugs like citalopram which were investigated with regard to their applicability for the PHIP technique and the possibility to achievernpolarization transfer to 13C nuclei. The last investigated substrate is a polymerizable monomer whose polymer was used as a blood plasma expander for trauma victims after the first half of the 20th century. In this case, the utility of the monomer for the PHIP technique as a basis for later investigations of a polymerization reaction using hyperpolarized monomers was examined.rnrnHence, this thesis covers the optimization of the PHIP technology, hereby combining different fields of research like chemical and spectroscopical aspects, and transfers the results to applications of real biologally acitve compounds.

Advances in hardware and molecular design of polarizing agents for dynamic nuclear polarization

Die Kernmagnetresonanz (NMR) ist eine vielseitige Technik, die auf spin-tragende Kerne angewiesen ist. Seit ihrer Entdeckung ist die Kernmagnetresonanz zu einem unverzichtbaren Werkzeug in unzähligen Anwendungen der Physik, Chemie, Biologie und Medizin geworden. Das größte Problem der NMR ist ihre geringe Sensitivtät auf Grund der sehr kleinen Energieaufspaltung bei Raumtemperatur. Für Protonenspins, die das größte magnetogyrische Verhältnis besitzen, ist der Polarisationsgrad selbst in den größten verfügbaren Magnetfeldern (24 T) nur ~7*10^(-5).rnDurch die geringe inhärente Polarisation ist folglich eine theoretische Sensitivitätssteigerung von mehr als 10^4 möglich. rnIn dieser Arbeit wurden verschiedene technische Aspekte und unterschiedliche Polarisationsagenzien für Dynamic Nuclear Polarization (DNP) untersucht.rnDie technische Entwicklung des mobilen Aufbaus umfasst die Verwendung eines neuen Halbach Magneten, die Konstruktion neuer Probenköpfe und den automatisierten Ablauf der Experimente mittels eines LabVIEW basierten Programms. Desweiteren wurden zwei neue Polarisationsagenzien mit besonderen Merkmalen für den Overhauser und den Tieftemperatur DNP getestet. Zusätzlich konnte die Durchführbarkeit von NMR Experimenten an Heterokernen (19F und 13C) im mobilen Aufbau bei 0,35 T gezeigt werden. Diese Ergebnisse zeigen die Möglichkeiten der Polarisationstechnik DNP auf, wenn Heterokerne mit einem kleinen magnetogyrischen Verhältnis polarisiert werden müssen.rnDie Sensitivitätssteigerung sollte viele neue Anwendungen, speziell in der Medizin, ermöglichen.

Proton magnetic resonance with parahydrogen induced polarization : Imaging strategies and continuous generation

A major challenge in imaging is the detection of small amounts of molecules of interest. In the case of magnetic resonance imaging (MRI) their signals are typically concealed by the large background signal of e.g. the tissue of the body. This problem can be tackled by hyperpolarization which increases the NMR signals up to several orders of magnitude. However, this strategy is limited for 1H, the most widely used nucleus in NMR andrnMRI, because the enormous number of protons in the body screen the small amount of hyperpolarized ones.Here, I describe a method giving rise to high 1H MRI contrast for hyperpolarized molecules against a large background signal. The contrast is based on the J-coupling induced rephasing of the NMR signal of molecules hyperpolarized via parahydrogen induce polarization (PHIP) and it can easily be implemented in common pulse sequences.rnrnHyperpolarization methods typically require expensive technical equipment (e.g. lasers or microwaves) and most techniques work only in batch mode, thus the limited lifetime of the hyperpolarization is limiting its applications. Therefore, the second part of my thesis deals with the simple and efficient generation of an hyperpolarization.These two achievements open up alternative opportunities to use the standard MRI nucleus 1H for e.g. metabolic imaging in the future.

Parahydrogen induced polarization on a clinical MRI system : polarization transfer of two spin order

Hyperpolarization techniques enhance the nuclear spin polarization and thus allow for new nuclear magnetic resonance applications like in vivo metabolic imaging. One of these techniques is Parahydrogen Induced Polarization (PHIP). It leads to a hyperpolarized 1H spin state which can be transferred to a heteronucleus like 13C by a radiofrequency (RF) pulse sequence. In this work, timing of such a sequence was analyzed and optimized for the molecule hydroxyethyl propionate. The pulse sequence was adapted for the work on a clinical magnetic resonance imaging (MRI) system which is usually equipped only with a single RF transmit channel. Optimal control theory optimizations were performed to achieve an optimized polarization transfer. A drawback of hyperpolarization is its limited lifetime due to relaxation processes. The lifetime can be increased by storing the hyperpolarization in a spin singlet state. The second part of this work therefore addresses the spin singlet state of the Cs-symmetric molecule dimethyl maleate which needs to be converted to the spin triplet state to be detectable. This conversion was realized on a clinical MRI system, both by field cycling and by two RF pulse sequences which were adapted and optimized for this purpose. Using multiple conversions enables the determination of the lifetime of the singlet state as well as the conversion efficiency of the RF pulse sequence. Both, the hyperpolarized 13C spin state and the converted singlet state were utilized for MR imaging. Careful choice of the echo time was shown to be crucial for both molecules.