<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>

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.

Thesis (Ph.D.); Submitted to the University of California Berkeley, Berkeley, CA (US); 1 Jun 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56278" Burke, Jason Timothy. USDOE Director. Office of Science. Office of High Energy and Nuclear Physics. Division of Nuclear Physics (US) 06/01/2004. Report is also available in paper and microfiche from NTIS.

Dans ce travail de thèse, nous illustrons la pertinence de la technique de photoémission pour l'étude des propriétés électroniques des matériaux. Dans la première partie, nous détaillons le développement et la phase de tests d'un nouveau bâti expérimental composé d'une chambre d'épitaxie par jets moléculaires (MBE) ainsi que d'une chambre de photoémission résolue en angle et en spin (SR-ARPES), connecté au tube Daum à l'Institut Jean Lamour. Les hautes performances de ce nouveau dispositif sont d'une part évaluées par une série de mesures expérimentales sur un système connu de la littérature (état de Shockley à la surface de l'Au(111)), et d'autre part illustrées par l'analyse de matériaux originaux (isolants topologiques, effet Kondo moléculaire …). Les valeurs de résolution en énergie sont inférieures à 2 meV et 300 meV pour la photoémission utilisant les rayonnements UV (UPS) et X (XPS) respectivement. La résolution angulaire est quant à elle meilleure que 0,2° et la température minimale atteignable est de 8,7 K. Finalement, des premières mesures de SR-ARPES ont démontré la capacité de ce nouveau bâti à mesurer les détails les plus fins de la structure de bandes polarisée en spin, se rapprochant ainsi de l'état de l'art dans le domaine. Ce nouveau dispositif est donc pleinement opérationnel. La seconde partie est consacrée à l'étude d'un oxyde de silicium ultra-mince bidimensionnel (2D) à la surface d'un substrat monocristallin de Ru(0001). Nous étudions tous les stades de croissance en partant du substrat nu de Ru(0001) jusqu'à une bicouche cristalline de cet oxyde, par XPS haute résolution (rayonnement synchrotron) et photoémission résolue en angle (ARPES). Nous confirmons la structure atomique établie dans la littérature pour ce système à la monocouche, avec en particulier l'existence de deux types de liaisons inéquivalentes Si-O-Ru révélées par des mesures inédites d’XPS haute résolution au niveau de la raie de cœur de l'O1s. En outre, nos mesures ARPES mettent en évidence l'existence d'états dispersifs bidimensionnels propres à ce matériau 2D. Alors que la monocouche est fortement connectée au substrat de ruthénium (liaisons covalentes), la bicouche en est déconnectée (liaisons de van der Waals). Notre étude confirme l'existence d’une telle transition avec des signatures claires à la fois en XPS et en ARPES, démontrant notamment la disparition des liaisons Si-O-Ru. Nous démontrons également la robustesse de ce système, qui une fois cristallisé peut être remis à l'air sans modifications majeures de ses propriétés électroniques, lui donnant ainsi un fort potentiel de fonctionnalisation (par exemple au sein d'hétérostructures 2D complexes comme couche isolante). Finalement, dans une troisième partie nous nous intéressons aux aspects théoriques de la photoémission résolue en angle. Alors que la structure de bandes est périodique dans l'espace réciproque, ce n'est pas le cas de l'intensité de photoémission, qui peut présenter des variations complexes dépendant de nombreux paramètres. Ces aspects sont généralement mal compris par les expérimentateurs. Nous présentons ici un modèle simple récemment proposé qui s'inscrit dans une description en trois étapes du processus de photoémission, et qui permet d'évaluer les éléments de matrice à un électron. Ces éléments de matrice représentent l'ingrédient essentiel permettant de comprendre la répartition du poids spectral en photoémission. Nous démontrons que dans ce modèle ils sont proportionnels à la transformée de Fourier de l'état de Wannier du système considéré, ainsi qu'à un terme de polarisation contenant les effets géométriques inhérents à toute expérience de photoémission. Nous appliquons alors cette approche à des systèmes physiques comme le graphène, ou encore au cas de mesures de dichroïsme circulaire réalisées au niveau des états d et de l'état de Shockley d'un monocristal de Cu(111), mettant ainsi en évidence ses succès et ses limitations / In this work, we highlight the relevance of photoemission spectroscopy for investigating the electronic properties of materials. In the first part, we tackle the development and the test phase of a new experimental setup which is composed of a molecular beam epitaxy (MBE) and a spin and angle resolved photoemission (SR-ARPES) chambers, connected to the tube at the Institut Jean Lamour. The high performances of this new setup are evaluated. On one hand by measuring well known system from the litterature (Shockley state at the Au(111) surface) and on the other hand by studying materials with novel properties (topological insulators, molecular Kondo effect …). Energy resolution is better than 2 meV for UV photoemission (UPS) and 300 meV for X-ray photoemission (XPS). We also have an angular resolution better than 0.2° and a lowest sample temperature of 8.7 K. Finally, first SR-ARPES measurements demonstrate the ability of this new installation to measure finest details of the spin polarized band structure. In short, this new setup is fully operationnal. The second part is dedicated to the study of a two dimensionnal (2D) ultra thin silicon oxide at the surface of a cristalline Ru(0001) substrate. Both growth and electronic properties are studied by high resolution XPS and ARPES. We confirm the structural model accepted for the system in the litterature for the monolayer case. In particular we confirm the existence of two inequivalent Si-O-Ru bonds with unprecedented high resolution XPS measurements on the O1s core level. In addition, our ARPES measurements highlight new dispersives states with 2D character which are unambiguously attributed to this oxide. While the monolayer is strongly connected to the ruthenium substrate (covalent bonds), the bilayer is disconnected from this latter one (van der Waals). Our work confirms the existence of such a transition with unambiguous signatures both in XPS and ARPES, in particular with the breaking of Si-O-Ru bonds. We also demonstrate the robustness of this system which, after being cristallised, can go to atmosphere without fundamental modification of his electronic properties. That gives a lot of potential applications to this 2D cristalline oxide, which could play in the futur the role of a wide band gap insulator in 2D heterostructures. In the last part, we focus on the theoretical aspects of photoemission. While band structure is periodic in the reciprocal space, it is not the case of photoemission intensity which can depend on a lot of parameters. We are motivated by the fact that these considerations are generally not well understood by experimentalists. Here, we present a simple model recently proposed in the three step approach of the photoemission process. With this model we can evaluate the one-electron matrix elements which play a key role to understand the variations of spectral weight in photoemission. In this approach, one-electron matrix elements are proportionnal to both Fourier transform of the Wannier state of the system and to a polarization term. We apply this model to « real » systems, in particular to graphene and to circular dichroism measurements on Cu(111) sample, highlighting sucess and limitations of this model