The electron is known to possess an anomalous magnetic moment, which interacts with the gradient of the electric field. This makes it necessary to compute its effects on the energy spectrum. Even though the Coulomb Dirac equation can be solved in closed form, this is no longer possible when the anomalous magnetic moment is included. In fact the interaction due to this term is so strong that it changes the domain of the Hamiltonian. From a differential equation point of view, the anomalous magnetic moment term is strongly singular near the origin. As usual, one has to resort to perturbation theory. This, however, only makes sense if the eigenvalues are stable. To prove stability is therefore a challenge one has to face before actually computing the energy shifts. The first stability results in this line were shown by Behncke for angular momenta κ ≥ 3, because the eigenfunctions of the unperturbed Hamiltonian decay fast enough near the origin. He achieved this by decoupling the system and then using the techniques available for second order differential equations. Later, Kalf and Schmidt extended Behncke’s results basing their analysis on the Prüfer angle technique and a comparison result for first order differential equations. The Prüfer angle method is particularly useful because it shows a better stability and because it obeys a first order differential equation. Nonetheless, Kalf and Schmidt had to exclude some coupling constants for κ > 0. This I believe is an artefact of their method. In this study, I make increasing use of asymptotic integration, a method which is rather well adapted to perturbation theory and is known to give stability results to any level of accuracy. Together with the Prüfer angle technique, this lead to a more general stability result and even allows for an energy shifts estimate. Hamiltonians traditionally treated in physics to describe the spin-orbit effect are not self adjoint i.e. they are not proper observables in quantum mechanics. Nonetheless, naive perturbation theory gives correct results regarding the spectrum. To solve this mystery, one has to study the nonrelativistic limit of the Dirac operator. In the second part of this study, I have not only given the higher order correction to the Dirac operator but also shown the effects of the spin-orbit term.

Made available in DSpace on 2017-07-21T19:25:51Z (GMT). No. of bitstreams: 1 Ramon F Costa.pdf: 10031939 bytes, checksum: 0a248edab54bf52531ad1b840500611c (MD5) Previous issue date: 2016-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we present the Aharonov-Bohm effect, as well as its implications. We also present the self-adjoint extension, an important tool in quantum mechanics. This work's main objective is to investigate the relation between the self-adjoint extension parameter and the Aharonov-Bohm system's parameters. Of particular interest is the relation between the self-adjoint extension parameter and the electron's anomalous magnetic dipole moment. This is done by comparison between two self-adjoint extension methods: Bulla-Gesztesy's and Kay-Studer's. We obtain the mathematical relation between the aforementioned quantities and conclude that the chosen methods are suitable to accomplish our goals. / Neste trabalho é apresentado o efeito e sistema de Aharonov-Bohm, além de suas implicações. Trata-se também da extensão autoadjunta de operadores em mecânica quântica. O principal objetivo é a investigação da relação entre o parâmetro da extensão autoadjunta do Hamiltoniano do sistema de Aharonov-Bohm, que tem origem matemática, e a física desse sistema. Interesse particular é dado à busca da relação entre o parâmetro da extensão e a anomalia do momento magnético do elétron. Para tal são usados dois métodos de extensão autoadjunta: o de Bulla-Gesztesy e o de Kay-Studer. A expressão matemática procurada é obtida, além de expressões para as energias dos estados ligados do sistema. Conclui-se que os métodos utilizados são adequados para atingir os objetivos propostos.

Vacuum polarization integral involves the vector spectral functions which can be experimentally determined. As the dominant uncertainty source to the integral, the precision measurement of the %born cross section of $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ as a function of energy from $2\pi$ threshold to 3GeV is performed by taking the ratio of $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ cross section to $e^+e^-\rightarrow\mu^+\mu^-(\gamma)$ cross section which are both measured with {\babar\ }data using ISR method in one analysis. Besides that taking the ratio of the cross sections of the two processes can cancel several systematic uncertainties, the acceptance differences between data and MC are measured using the same data, and the corresponding corrections are applied on the efficiencies predicted by MC which can control the uncertainties. The achieved final uncertainty of the born cross section of $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ in $\rho$ mass region ($0.6\sim0.9$GeV) is 0.54\%. As a consequence of the new vacuum polarization calculation using the new precision result of the $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ cross section, the impact on the SM prediction of muon anomalous magnetic moment $g-2$ is presented, which is also compared with other data based predictions and direct measurement.

Les moments magnétiques anomaux des leptons ont joué un rôle important dans le développement du modèle standard de la physique des particules. Aujourd’hui, celui du muon est mesuré très précisément et le sera avec une precision encore plus grande par une expérience qui débutera en 2017. Dans la mesure où la prédiction théorique pourra être faite avec des incertitudes comparables, un test rigoureux du modèle standard sera possible. Nous étudions ici le facteur limitant de cette prédiction, la contribution de la polarisation hadronique du vide à l’ordre dominant (HVP-LO). Nous calculons cette contribution numériquement à l’aide d’une version discrétisée de la théorie de l’interaction forte, la chromodynamique quantique sur réseau. Le calcul haute-performance permet de résoudre la théorie dans son régime hautement non-linéaire qui est le plus pertinent ici. Les algorithmes de simulation et les méthodes utilisées pour obtenir la polarisation hadronique, ainsi que les incertitudes associées, sont décrits. Ces méthodes sont ensuite appliquées à des simulations réalisées avec la collaboration Budapest-Marseille-Wuppertal. Dans un premier temps, elles sont implémentées dans une étude dédiée des effets de volume fini. Les méthodes les plus robustes sont ensuite utilisées pour calculer la polarisation hadronique avec des simulations qui comprennent N_f=2+1+1 saveurs de quarks. Celles-ci sont réalisées directement à la valeur physique des masses de quarks u, d, s et c, avec six tailles de maille et dans de gros volumes de 6 fm^3. Elles nous permettent de calculer la contribution HVP-LO au moment magnétique anomal du muon avec des erreurs contrôlées d’environ 3%. / The anomalous magnetic moments of leptons have played an important role in the development of the Standard Model of particle physics. Today, that of the muon is measured very precisely and will be so with even higher precision in an experiment that will begin in 2017. To the extent that the theoretical prediction can be made with comparable uncertainties, a rigorous test of the Standard Model will be possible. Here we study the limiting factor in this prediction, the leading-order hadronic vacuum polarization contribution (HVP-LO). We compute this contribution numerically with a discretized version of the theory of the strong interaction: lattice Quantum Chromodynamics. High-performance computing allows to solve the theory in its highly nonlinear regime, which is the one most relevant here. The simulation algorithms and the methods used to obtain the HVP, as well as the associated statistical and systematic uncertainties, are described. These methods are then applied to simulations performed with the Budapest-Marseille-Wuppertal collaboration. First they are implemented in a dedicated study of finite-volume effects. The most robust methods are then used to compute the HVP with simulations which include N_f=2+1+1 flavors of quarks. These are performed directly at the physical values of the u, d, s and c quark masses, with six lattice spacings and in large volumes of 6 fm^3. They allow us to compute the HVP-LO contribution to the anomalous magnetic moment of the muon with controlled errors of around 3%.

Wir stellen die Resultate einer Untersuchung von Strom-Strom-Korrelatoren beruhend auf den Grundprinzipien der Quantenchromodynamik vor. Wir benutzen die nicht-perturbativen Methoden der sogenannten twisted mass Gitter-QCD mit dynamischem up- und down-Quark unter Ausnutzung der automatischen O(a)-Verbesserung. Als Anwendung diskutieren wir die Berechnung des hadronischen Beitrags zur Korrektur in führender Ordnung in der elektromagnetischen Kopplung zum anomalen magnetischen Moment des Myons. Dieses gilt als eine sehr geeignete Größe für die aktuelle Suche nach neuer Physik jenseits des Standardmodells, besonders im Hinblick auf die Diskrepanz zwischen der Vorhersage aus dem Standardmodell und dem experimentell gemessenen Wert. Innerhalb der theoretischen Bestimmung ist der hadronische Anteil führender Ordnung mit der größten Unsicherheit behaftet und genießt derzeit somit naturgemäß Priorität. Wir beschreiben unsere Studie aller systematischen Unsicherheiten der Gitterrechnung auf Grundlage von drei Gittervolumina, zwei Gitterabständen, Pionmassen im Bereich von 650 MeV bis 290 MeV und den Quark-unverbundenen Beiträgen. Für die Extrapolation zum physikalischen Punkt stellen wir eine neue Methode vor, welche die Abhängigkeit von der Pionmasse hinreichend abschwächt und eine lineare Extrapolation ermöglicht. Im Ergebnis bestimmen wir den Beitrag von up- und down-Quark zu a_mu^hlo(N_f=2) = 5.69 (15) 10^(-8). Die dargelegten Methoden werden auf das Elektron- und das Tau-Lepton erweitert mit dem Resultat a_el^hlo(N_f=2) = 1.512 (43) 10^(-12) bzw. a_tau^hlo(N_f=2) = 2.635 (54) 10^(-6). Wir schätzen den Beitrag des charm-Quarks zu a_mu^hlo in der Partially Quenched tmLQCD mit dem Resultat a_mu^hlo(charm) = 1.447 (24) (30) 10^(-9) in Übereinstimmung mit der Vorhersage über die Dispersionsrelation unter Hinzunahme experimenteller Daten für das hadronische R-Verhältnis. / We present an investigation of hadronic current-current correlators based on the first principles of Quantum Chromodynamics. Specifically we apply the non-perturbative methods of twisted mass lattice QCD with dynamical up and down quark taking advantage of its automatic O(a) improvement. As a special application we discuss the calculation of the hadronic leading order contribution to the muon anomalous magnetic moment. The latter is regarded as a promising quantity for the search for physics beyond the standard model. The origin of the strong interest in the muon anomaly lies in the persistent discrepancy between the standard model estimate and its experimental measurement. In the theoretical determination the hadronic leading order part is currently afflicted with the largest uncertainty and a dedicated lattice investigation of the former can be of strong impact on future estimates. We discuss our study of all systematic uncertainties in the lattice calculation, including three lattice volumes, two lattice spacings, pion masses from 650 MeV to 290 MeV and the quark-disconnected contribution. We present a new method for the extrapolation to the physical point that softens the pion mass dependence of a_mu^hlo and allows for a linear extrapolation with small statistical uncertainty at the physical point. We determine the contribution of up and down quark as a_mu^hlo(N_f=2) = 5.69 (15) 10^(-8). The methods used for the muon are extended to the electron and tau lepton and we find a_el^hlo(N_f=2) = 1.512 (43) 10^(-12) and a_tau^hlo(N_f=2) = 2.635 (54) 10^(-6). We estimate the charm contribution to a_mu^hlo in partially quenched tmLQCD with the result a_mu^hlo(charm) = 1.447 (24) (30) 10^(-9) in very good agreement with a dispersion-relation based result using experimental data for the hadronic R-ratio.

Les effets cohérents dans l’interaction des particules à haute énergie avec les cristauxouvrent de nouvelles opportunités d’accélération et détection de particules. Les champs électromagnétiquesefficaces présents dans les cristaux qui se présentent dans ce cas peuvent dépassermille fois les champs qui sont maintenant réalisables dans les installations expérimentales.La première partie de la thèse est consacrée à l’étude théorique des effets de diffusion multiples surla dynamique et le rayonnement des particules chargées de haute énergie dans les cristaux. L’undes objectifs de cette étude est de trouver des conditions optimales pour effectuer la mesure dumoment magnétique anormal du baryon Lamda au LHC. En raison de la courte durée de vie de cetteparticule, le seul moyen de fournir une telle mesure est d’utiliser un cristal courbé, qui peut imiter lechamp magnétique de l’ordre de milliers de Tesla.L’optimisation des paramètres du set up expérimental a été réalisée sur la base de la simulation parordinateur du passage du Baryon Lamda à travers un cristal courbé à l’aide du modèle de collisions binaires, entenant compte de la diffusion incohérente sur les vibrations thermiques des atomes des noeuds enréseau et de la diffusion sur un sous-système électronique d’un cristal. Les résultats de la recherchemenée dans la thèse démontre la possibilité d’effectuer une telle expérience au LHC et sont devenusla base de la proposition correspondante.Les effets de diffusion multiple des électrons ultra relativistes et le rayonnement des positons dansles cristaux alignés sont également considérés dans la première partie de la thèse.Il est également démontré que la distribution angulaire spectrale et les caractéristiques de polarisationdu rayonnement diffèrent essentiellement des résultats de la théorie de Bethe–Heitler. Lesconditions d’observation expérimentale de ces effets sont présentées.La deuxième partie de la thèse est consacrée à l’étude des processus transitoires des réacteursrapides fonctionnant dans un régime d’onde de combustion nucléaire auto-entretenue (OCN). C’estun nouveau concept de réacteurs de fission nucléaire avec la soi-disant “sécurité intrinsèque”, danslaquelle le développement d’une réaction nucléaire à chaîne incontrôlable est impossible en raisondes principes physiques du fonctionnement du réacteur. Les concepts prometteurs du réacteur OCNdans le cas de sa mise en œuvre permettent d’utiliser l’uranium appauvri et fournit le traitement desdéchets radioactifs à longue durée de vie.Cette étude est basée sur la résolution numérique de l’équation de diffusion non linéaire non stationnairedu transport de neutrons avec un ensemble d’équations de combustion pour les composantsdu carburant et les équations de la cinétique nucléaire pour les noyaux précurseurs des neutronsretardés, en utilisant une approche “effective multigroup”. Le modèle du réacteur cylindrique homogèneavec le combustible métallique des cycles de carburant U–Pu, Th–U et mixte Th–U–Pu estconsidéré dans le cadre du concept de flambage.À la suite de ces études, l’existence du mode OCN dans le cas du combustible mixte Th–U–Puet de ses avantages essentiels est démontrée; l’analyse détaillée d’un type spécial de rétroactionnégative inhérente au régime OCN et sous-jacente à la “sécurité intrinsèque” d’un tel réacteur esteffectuée; les scénarios d’un démarrage en douceur, d’un arrêt forcé et d’un redémarrage ultérieurdu réacteur OCN sont développés. / The coherent effects in the high energy particle interaction with crystals open up new opportunities for accelerating and detecting techniques. The effective electromagnetic fields that arise in this case can exceed a thousand times the fields that are now attainable at experimental installations. The first part of the thesis is devoted to the theoretical study of the multiple scattering effects on the dynamics and radiation of high energy charged particles in crystals. One of the goals of this study is to find optimal conditions to carry out the measurement of the anomalous magnetic moment of the charmed Lambda Baryon at the LHC. Due to the short lifetime of this particle the only way to provide such a measurement is to use a bent crystal, which can imitate the magnetic field of order of thousand Tesla. The optimization of the parameters for an experimental setup was carried out on the basis of computer simulation of the Lamda Baryon passage through a bent crystal using the binary collisions model, taking in to account incoherent scattering on thermal vibrations of atoms at lattice nodes, and scattering on an electronic subsystem of a crystal. The results of the research conducted in the thesis give an optimistic forecast for the possibility of carrying out such an experiment at the LHC and became the basis of the corresponding proposal. The multiple scattering effects of the thesis. This study is performed in the framework of classical electrodynamics approach for describing the relativistic particle radiation and the computer simulation of fast charged particles passing through a crystal using the above-mentioned model. It is shown, that the spectral-angular distribution and the polarization characteristics of radiation essentially differ from the results of the Bethe–Heitler theory. The conditions for the experimental observation of these effects are presented. The second part of the thesis is devoted to the study of transient processes in advanced fast reactor breeder working in a self-sustained nuclear burning wave (NBW) regime. It is a new concept of nuclear fission reactors with the so-called “intrinsic safety”, in which the development of uncontrolled chain nuclear reaction is impossible due to the physical principles of reactor operation. The promising concepts of NBW reactor in the case of its implementation allows to utilize the depleted Uranium and provides the treatment of long-lived radioactive waste. This study is based on numerical solving the non-stationary non-linear diffusion equation of neutron transport together with a set of the burn-up equations for fuel components and the equations of nuclear kinetics for precursor nuclei of delayed neutrons using effective multi-group approach. The model of cylindrical homogeneous reactor with metallic fuel of U–Pu, Th–U and mixed Th–U–Pufuel cycles is considered in the framework of the buckling concept. As a result of these studies the existence of the NBW mode in the case of mixed Th–U–Pu fuel and its essential advantages are demonstrated; the detailed analysis of a special kind of the negative reactivity feedback that is inherent to the NBW regime and underlies the “intrinsic safety” of such a reactor is performed; the scenarios of a smooth start-up, forced shutdown and subsequent restart of the NBW reactor are developed.