<p> This thesis presents a derivation of a method to obtain two-body, diagonal and non-diagonal, reaction matrix elements for central and tensor forces respectively directly from nucleon-nucleon scattering phase shifts. This procedure eliminates the necessity for constructing a nuclear potential.</p> / Thesis / Master of Science (MSc)

We present a calculation of vector and axial-vector form factors for each of the octet hyperon semi-leptonic transition matrix elements by using the techniques of lattice QCD where simulations were performed with Nf = 2 + 1 flavours of dynamical O(a)-improved Wilson fermions. We also study the electromagnetic form factors, axial charges and other properties of octet baryons. Errors due to extrapolation to zero transferred momentum are reduced by applying a twist to the boundary conditions on the lattice. Our form factor results compare favourably with experiment and other lattice QCD determinations. By considering an expansion about the SU(3)-flavour symmetric limit we seek to investigate and quantify the symmetry breaking effects in these matrix elements due to the mass splitting between the strange and light quarks. We find good agreement with the Ademollo-Gatto theorem for the vector form factor, a measurable amount of breaking in the axial-vector form factor and significant effects in the weak magnetism form factor. Knowledge of the parameterisation of SU(3)-flavour symmetry breaking allows for a series of constrained fits to be made to the form factor results which are used to arrive at a 'baryonic' estimation of the Cabibbo-Kobayashi-Maskawa matrix element |Vus|.

The flavor changing neutral current process b → dγ is a sensitive probe to the Standard Model of elementary particle physics. Using a sample of 386 × 10⁶ B meson pairs accumulated by the Belle detector at the KEKB e⁺e⁻ collider, we measure the branching fractions for the exclusive modes B⁻ → ρ⁻γ, B̅⁰ → ρ⁰γ and B̅⁰ → ωγ as follows: B(B⁻ → ρ⁻γ) = 0.55 _−0.36^+0.42_−0.08^+0.09 B(B̅⁰ → ρ⁰γ) = 1.25 _−0.33^+0.37_−0.06^+0.07 B(B̅⁰ → ωγ) = 0.56 _−0.27^+0.34_−0.10^+0.05 where the first error on each value is statistical and the second is systematic. Assuming that these three modes are related by isospin conservation rules, we find the combined branching fraction B(B̅ → (ρ,ω)γ) = 1.32 _−0.31^+0.34_−0.09^0.10. This result is used to determine the ratio of CKM matrix elements, |V_td/V_ts| = 0.199 _−0.025^+0.026_−0.015^0.018. / Ph. D.

We consider the finite two-dimensional Ising model on a lattice with periodic boundaryconditions. Kaufman determined the spectrum of the transfer matrix on the finite,periodic lattice, and her derivation was a simplification of Onsager's famous result onsolving the two-dimensional Ising model. We derive and rework Kaufman's resultsby applying representation theory, which give us a more direct approach to computethe spectrum of the transfer matrix. We determine formulas for the spin correlationfunction that depend on the matrix elements of the induced rotation associated withthe spin operator. The representation of the spin matrix elements is obtained byconsidering the spin operator as an intertwining map. We wrap the lattice aroundthe cylinder taking the semi-infinite volume limit. We control the scaling limit of themulti-spin Ising correlations on the cylinder as the temperature approaches the criticaltemperature from below in terms of a Bugrij-Lisovyy conjecture for the spin matrixelements on the finite, periodic lattice. Finally, we compute the matrix representationof the spin operator for temperatures below the critical temperature in the infinite-volume limit in the pure state defined by plus boundary conditions.

Precise predictions of hadronic matrix elements in heavy meson decays are important to constrain the fundamental parameters in the Standard Model of particle physics. The CKM matrix element Vub can be extracted from experimental data on the decay B → πℓν if the hadronic form factor is known. In addition, loop suppressed rare decays of B-mesons, such as B → K∗γ and B → K(∗)ℓℓ, provide valuable insight into new physics models. Hadronic form factors for exclusive meson decays can be calculated in the framework of lattice QCD. As the wavelength of heavy quarks is not resolved on currently available lattices I use an effective nonrelativistic theory to discretise the heavy degrees of freedom. In addition, the discretisation errors in the final state meson are reduced by working in a moving frame. I review the phenomenology of rare B decays and describe how lattice QCD can contribute to calculating the relevant form factors. As the short distance physics in the effective theory is different from that of QCD, the Lagrangian and decay currents need to be renormalised. I show how this can be achieved in the framework of lattice perturbation theory. I calculate the perturbative renormalisation constants of the leading order operators in the heavy quark Lagrangian. Motivated by nonperturbative studies I extend this approach to higher order kinetic terms which break rotational invariance. In combination with simulations in the weak coupling regime of the theory, results from diagrammatic lattice perturbation theory are used to calculate the heavy quark selfenergy corrections and predict the fundamental parameters of QCD. I calculate the one loop correction on a finite lattice with twisted boundary conditions which is used for the extraction of higher order perturbative corrections. I renormalise the heavy-light current to one loop order in lattice mNRQCD and present results from nonperturbative studies. Finally, I discuss how the results are used in the calculation of hadronic form factors.

Density functional theory is a preferred microscopic method for calculation of nuclear properties over the whole nuclear chart. Besides ground-state properties, which are calculated by Hartree-Fock theory, nuclear excitations can be described by means of Random Phase Approximation (RPA). The main objective of the present work is to give the RPA formalism for spherically symmetric nuclei, using the techniques of angular-momentum coupling. Various auxiliary topics, such as Hartree-Fock theory, Coulomb integral, center-of-mass corrections and pairing, are treated as well. RPA method is derived also for axially deformed nuclei. The derived formulae are then implemented in the computer code and utilized for calculation of some physical results. After thorough investigation of the precision aspects of the calculation, the following topics are treated as examples: toroidal nature of the low-energy (pygmy) part of the E1 resonance, giant resonances of various multipolarities in deformed nucleus 154Sm, and magnetic dipole (M1) transitions in deformed 50Cr. Powered by TCPDF (www.tcpdf.org)

Atomic parity violation measurements provide a way to probe physics beyond the Standard Model. They can provide constraints on conjectures of a massive Z′ bosonor a light boson, or searches of dark energy. Using the two-pathway coherent control technique, our group plans to make a new measurement of the weak interaction induced parity non-conservation (PNC) transition moment (<i>E_PNC</i>) on the cesium 6S→7S transition. We will coherently interfere a 2-photon transition with the Stark and PNC transitions to amplify and extract the PNC amplitude. Previously, our lab has measured the magnetic dipole transition moment on the same 6S→7S transition to about 0.4% uncertainty using this technique. In this dissertation, I discuss improvements made to the system, and review what future upgrades are needed for a new<i> E</i>_{<i>PNC </i>}measurement. Key systematics are also described. For an accurate determination of <i>E_PNC</i>, properties of cesium such as the scalar (<i>α</i>) and vector (<i>β</i>) transition polarizabilities are needed. I present improved determinations of keyelectric dipole matrix elements, and calculate new high precision determinations of <i>α</i> and <i>β</i>. Finally, using <i>β</i> and the previously measured value of <i>E_PNC/β</i>, I calculate new values for the weak charge of the cesium nucleus Q_w.<br>

Diese Arbeit befasst sich mit der Konstruktion verbesserter interpolierender Mesonenfelder in der Gitter-QCD. Sie hat das primäre Ziel, Korrelationsfunktionen mit einem deutlich reduzierten Beitrag des ersten angeregten Mesonenzustandes zu erhalten, um eine sicherere Bestimmung von Massen und Zerfallskonstanten der Mesonen zu ermöglichen. Eine Basis solcher interpolierender Mesonen-Randfelder wird im Schrödinger Funktional in der gequenchten Approximation benutzt. Verbesserte interpolierende Felder zur Bestimmung spektraler Eigenschaften leichter pseudoskalarer Mesonen sowie des B--Mesonensystems (letzteres wird in führender Ordnung der HQET behandelt) werden auf mehreren Wegen gewonnen. Ein Hilfsmittel, verbesserte Felder zu konstruieren, ist das Variationsprinzip. Es wird auf Matrizen von Rand-Rand-Korrelationsfunktionen angewandt. Darüber hinaus werden alternative Analysemethoden vorgestellt. Sie erlauben sowohl die Abschätzung der Grundzustandsenergie als auch der Energielücke zum ersten radial angeregten Zustand. Die Untersuchung des B-Mesonensystems ist in vielfacher Hinsicht interessant. Zum einen werden sie in sogenannten B-Fabriken, wie z. B. im BaBar- und Belle-Experiment, in grosser Zahl erzeugt, um ihre charakteristischen Eigenschaften (Masse, Zerfallsbreiten, CP-Symmetrie verletzende Zerfälle usw.) genau zu messen. Zum anderen müssen die von der Theorie vorhergesagten auftretenden Phänomene, wie z. B. die CP-Verletzung, auch verstanden werden. Die Methoden der Gittereichtheorie können unter anderem dabei helfen, bestehende Unsicherheiten in CKM-Matrixelementen durch nicht-perturbative Bestimmungen hadronischer Massen, Zerfallskonstanten usw. zu reduzieren. / The general aim of this thesis is to probe several methods to extract low-energy quantities (masses, decay constants, ...) more reliably in lattice gauge theory. We will investigate how to suppress contributions to correlation functions from the first excited meson state. We will show how to construct so-called improved meson interpolating fields, as they have only small contributions from the first excited meson state, from a basis of interpolating fields at the Schrödinger functional boundaries. The variational principle is applied to correlation matrices that are built up from boundary-to-boundary correlation functions. It will deliver information about the lowest-lying meson states in the considered channel. We also investigate the possibility to cancel the first excited state contribution by means of an alternative method. Moreover, an alternative way to extract the mass gap between the ground and the first excited state will be presented. Monte-Carlo simulations at several lattice spacings are performed in the ''quenched approximation''. Spectral properties of light-light and static-light pseudoscalar mesons are investigated. The first type is realised by two mass-degenerate quarks at about the strange quark mass, the second type by a light quark with the mass of the strange quark and an infinitely heavy b-quark. The light-light channel describes unphysically heavy pions and the static-light one is an approximation for the Bs-meson. The investigation of the latter case is particularly interesting since so-called B--factories, such as BaBar and Belle, are gathering physical information about masses, decay modes and CP--violating effects in the B--meson system.

This thesis is devoted to the optical properties of low-dimensional structures based on such two-dimensional materials as graphene, silicene and phosphorene. We investigate optical properties of a variety of quasi-one dimensional and quasi-zero-dimensional structures, which are promising for future optoelectronics. Primarily we focus on their low-energy optical properties and how these properties are influenced by the structures’ geometry, external fields, intrinsic strain and edge disorder. As a consequence of this endeavor, we find several interesting effects such as correlation between the optical properties of tubes and ribbons whose periodic and ‘hard wall’ boundary conditions are matched and a universal value of matrix element in narrow-gap tubes and ribbons characterizing probability of transitions across the band gap opened up by intrinsic strain originating from the tube’s surface curvature or ribbon’s edge relaxation. The analytical study of the gapped 2D Dirac materials such as silicene and germanene, which have some similarity to the aforementioned quasi-one-dimensional systems in terms of physical description, reveals a valley- and polarization-dependent selection rules. It was also found that absorption coefficient should change in gapped materials with increasing frequency and become a half of its value for gap edge transitions when the spectrum is linear. Our analysis of the electronic properties of flat clusters of silicene and phosphorene relates the emergence and the number of the peculiar edge states localized at zero energy, so-called zero-energy states, which are know to be of topological origin, to the cluster’s structural characteristics such as shape and size. This allows to predict the presence and the number of such states avoiding complicated topological arguments and provides a recipes for design of metallic and dielectric clusters. We show that zero-energy states are optically active and can be efficiently manipulated by external electric field. However, the edge disorder is important to take into account. We present a new fractal-based methodology to study the effects of the edge disorder which can be applied also to modeling of composite materials. These finding should be useful in design of optoelectronic devices such as tunable emitters and detectors in a wide region of electromagnetic spectrum ranging form the mid-infrared and THz to the optical frequencies.

Die Untersuchung von korrelationsinduzierten Effekten, wie beispielsweise der kollektiven magnetischen Ordnung, verlangt einen Einblick in die elektronische Struktur der Festkörper. Hier stehen mit den Ein-Teilchen-Spektroskopien (Photoemission und inverse Photoemission) sowie den Zwei-Teilchen-Spektroskopien (Auger-Elektronen- und Appearance-Potential-Spektroskopien) nützliche experimentelle Werkzeuge zur Verfügung. Eine adäquate Interpretation der experimentell ermittelten Spektren erfordert die Berücksichtigung (i) der elektronischen Korrelationen, (ii) der orbitalen Entartung sowie (iii) der Übergangsmatrixelemente. Der vorliegenden Arbeit liegt ein Multiband-Hubbard-Modell zugrunde, das die Hopping- und Hybridisierungsprozesse der für die 3d-Übergangsmetalle relevanten Orbitale (4s-, 4p- und 3d-Orbitale) und die lokalen Coulomb-Wechselwirkungen der stark lokalisierten 3d-Elektronen beschreibt. Die Hopping- und Hybridisierungsparameter werden Bandstrukturrechnungen (lokale Dichteapproximation der Dichtefunktionaltheorie) entnommen. Als Ein-Teilchen-Basis werden quasiatomare Orbitale verwendet, deren hohe Symmetrie es erlaubt, die vollständige lokale 3d-Coulomb-Matrix mithilfe von lediglich drei Zahlen (effektive Slater-Parameter) zu parametrisieren. Fasst man die effektiven Slater-Parameter zu einer mittleren direkten Wechselwirkungsstärke U und einer mittleren Austauschwechselwirkungsstärke J zusammen, so sind U und J die beiden einzigen Parameter des Modells, die dann an experimentelle Daten (z.B. Spinmoment bei T=0K) angepasst werden können. Für die Berechnung der Ein-Teilchen-Green-Funktion, die die Photoemissionsspektren bestimmt, wird die Störungstheorie zweiter Ordnung um die Hartree-Fock-Lösung verwendet und damit die Magnetisierung als Funktion der Temperatur für Nickel berechnet. Die Kombination der errechneten Green-Funktion mit den Übergangsmatrixelementen der Photoemission gestattet dann einen quantitiven Vergleich mit experimentellen spin- und winkelaufgelösten Daten für endliche Temperaturen und verschiedene Photonenenergien. Die Zwei-Teilchen-Spektren lassen sich als Funktionale der Ein-Teilchen-Green-Funktion auffassen. Durch die Verwendung sogenannter Leiter-Näherungen werden nicht nur die Wechselwirkungen der an den Übergangsprozessen beteiligten Teilchen mit dem Restsystem (Selbstenergieeinschübe) berücksichtigt, sonderen auch die Wechselwirkungen der direkt am Prozess beteiligten Teilchen untereinander (Endzustandskorrelationen). Die Verwendung des Zwei-Stufen-Modells impliziert jedoch, dass die Valenzbandelektronen das Potential des zuvor erzeugten Core-Lochs abschirmen werden, was sich insbesondere auf die Auger-Spektren auswirkt. Am Beispiel der Appearance-Potential-Spektren wird die vielteilchentheoretisch berechnete Green-Funktion mit entsprechenden Übergangsmatrixelementen kombiniert. Die resultierenden Spektren sind für alle betrachteten Temperaturen in sehr guter Übereinstimmung mit gemessenen Spektren. / The investigation of correlation-induced effects, as for example the collective magnetic order, requires an insight into the electronic structure of solids. In this context the one-particle spectroscopies (photoemission and inverse photoemission) as well as the two-particle spectroscopies (Auger electron and appearance potential spectroscopies) represent useful experimental tools. An adequate interpretation of the experimentally determined spectra requires the consideration of (i) electronic correlations, (ii) orbital degeneration as well as (iii) transition-matrix elements. The present work uses a multi-band Hubbard model, which describes the hopping and hybridization processes of the relevant orbitals in the 3d-transition metals (4s, 4p and 3d orbitals) and the local Coulomb interactions of the strongly localized 3d electrons. The hopping and hybridization parameters are taken from band-structure calculations (local density approximation of the density functional theory). As one-particle basis quasi-atomic orbitals are used, whose high symmetry permits it to parameterize the complete local Coulomb-matrix among 3d-electrons by only three numbers (effective Slater parameters). If one combines the effective Slater parameters into an averaged direct interaction strength U and an averaged exchange interaction strength J, then U and J are the only parameters of the model, which can be fitted to experimental data (e.g. spin moment at T=0K). For the calculation of the one-particle Green function, which determines the photoemission spectra, the second order perturbation theory around the Hartree-Fock solution is used. Within this framework the magnetization as function of the temperature is calculated for nickel. The combination of the calculated Green function and the photoemission transition-matrix elements permits a quantitative comparison with spin- and angle-resolved measurements for finite temperatures and different photon energies. The two-particle spectra can be understood as functionals of the one-particle Green function. Due to the usage of so called ladder approximations one is able to account not only for the correlations between the considered particles and the remainder system (self-energy insertations) but also for the correlations among those particles directly involved in the transition (final state correlations). The usage of the two-step model implies, however, that the valence band electrons tend to screen the additional potential of the core hole created before, which in particular affects the Auger spectra. As an example, the appearance potential spectra of nickel are calculated by combining the corresponding Green function with appropriate transition-matrix elements. The resulting spectra are in a very good agreement with measured spectra for all temperatures.