Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O espalhamento píon-núcleon é um processo de grande importância para o conhecimento das interações fortes por vários motivos. A existência de ressonâncias em colisões píon-núcleon é compatível com o modelo de quarks. A determinação do termo sigma dá acesso as propriedades do núcleon e a constante de acoplamento π-N é fundamental para os cálculos em física nuclear. Nesta dissertação usamos um método para implementar a condição de unitariedade elástica em uma amplitude de baixas energias que reproduz os comprimentos de espalhamento obtidos por Weinberg. A partir da amplitude corrigida em unitaridade que construimos, estudamos as propriedades de simetria de cruzamento da amplitude total e a violação de isospin. Em seguida mostramos que as sucessivas correções de unitariedade se tornam cada vez menores, concluindo que o método utilizado permite construir amplitudes parciais de espalhamento que corrigem a unitariedade elástica perturbativamente. / The pion-nucleon interaction is an important source of knowledge of the strong interaction.The properties of the baryon resonances produced in pion-nucleon collisions give strong support to the quark model. The amplitude is related to the value of the pion-nucleon sigmaterm which constrains models of nucleon structure. The pion-nucleon coupling constant provides fundamental input for the calculation of nuclear forces.In this thesis a method is used to implement the elastic unitarity condition for a low energy amplitude reproducing the Weinberg scattering lengths. We study the total amplitude crossing symmetry properties and the isospin violation from electromagnetic mass diference of the corrected amplitude. Finally we show that the next order unitarity corrections are small,allowing us to conclude that the proposed method is a consistent perturbative scheme to implement elastic unitarity constraint.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O espalhamento píon-núcleon é um processo de grande importância para o conhecimento das interações fortes por vários motivos. A existência de ressonâncias em colisões píon-núcleon é compatível com o modelo de quarks. A determinação do termo sigma dá acesso as propriedades do núcleon e a constante de acoplamento π-N é fundamental para os cálculos em física nuclear. Nesta dissertação usamos um método para implementar a condição de unitariedade elástica em uma amplitude de baixas energias que reproduz os comprimentos de espalhamento obtidos por Weinberg. A partir da amplitude corrigida em unitaridade que construimos, estudamos as propriedades de simetria de cruzamento da amplitude total e a violação de isospin. Em seguida mostramos que as sucessivas correções de unitariedade se tornam cada vez menores, concluindo que o método utilizado permite construir amplitudes parciais de espalhamento que corrigem a unitariedade elástica perturbativamente. / The pion-nucleon interaction is an important source of knowledge of the strong interaction.The properties of the baryon resonances produced in pion-nucleon collisions give strong support to the quark model. The amplitude is related to the value of the pion-nucleon sigmaterm which constrains models of nucleon structure. The pion-nucleon coupling constant provides fundamental input for the calculation of nuclear forces.In this thesis a method is used to implement the elastic unitarity condition for a low energy amplitude reproducing the Weinberg scattering lengths. We study the total amplitude crossing symmetry properties and the isospin violation from electromagnetic mass diference of the corrected amplitude. Finally we show that the next order unitarity corrections are small,allowing us to conclude that the proposed method is a consistent perturbative scheme to implement elastic unitarity constraint.

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Dans ce travail de thèse est présentée l’analyse des électroproductions exclusives des mésons f ₀ (980) et f₂(1270) sur le proton. Les données ont été acquises pendant l’expérience e1-6 (2001-2002) avec le détecteur CLAS du Jefferson Lab aux États-Unis, en utilisant un faisceau de 5.754 GeV et une cible de dihydrogène. Nous avons mesuré pour la première fois au monde les sections efficaces réduites différentielles de ces deux processus, dans le domaine cinématique 1.5 < Q2 < 4.3 GeV2 et 0.15< xB < 0.55. Nous proposons une interprétation de nos résultats sur une approche basée sur des degrés de liberté hadronique et la théorie de Regge. Une analyse des données en termes d’amplitudes d’ondes partielles et en terme de moments des distributions angulaires a également été tentée. Enfin, nous avons effectué la calibration des photomultiplicateurs du détecteur central de neutron (CND) pour le détecteur CLAS12. Le CND a été optimisé pour l’étude du processus n-DVCS (Diffusion Compton Profondément Virtuelle du neutron). / We present in this report our results for the exclusive electroproductions of f₀(980) and f₂(1270) off the proton. The data were taken during the e1-6 experiment (2001-2002) with the CLAS detector of Jefferson Laboratory, using a 5.754 GeV beam and a liquid hydrogen target. We have measured for the first time the reduced differential cross sections for these two processes, in the kinematical region 1.5 < Q2 < 4.3 GeV2 and 0.15< xB < 0.55. We propose an interpretation of our results according to a Regge-based model. An alternative analysis of the data in terms of partial waves amplitudes as well as in terms of moments of the decay angular distributions has also been attempted. Finally, we have performed the calibration of the photomultipliers of the Central Neutron Detector (CND), to be installed in the CLAS12 detector. The CND has been optimized for the study of the n-DVCS process (Deeply Virtual Compton Scattering off the neutron).

Cette thèse traite de la résolution du problème direct de propagation d'un champ élastodynamique rayonné par une source dans un milieu stratifié anisotrope. Le contexte applicatif visé est le contrôle non destructif par ondes ultrasonores guidées de plaques de matériaux composites. Aux basses fréquences, ces matériaux sont assimilables à des milieux homogènes, anisotropes et dissipatifs. Deux approches causales sont étudiées et mises en oeuvre pour résoudre l'équation d'onde, et leur intérêt vis-à-vis de la méthode modale harmonique - la plus couramment employée dans ce domaine applicatif - est discuté. L'une des méthodes est modale et est formulée directement dans le domaine temporel. Elle permet de traiter facilement l'anisotropie, y compris en 3D, mais souffre des écueils classiques concernant le régime non-établi ou le cas du guide ouvert. L'autre approche est une formulation dans le domaine de Laplace de la méthode dite par ondes partielles. Elle présente l'intérêt d'être extrêmement polyvalente tout en conduisant à des coûts numériques tout à fait raisonnables. Dans un second temps, la possibilité d'exploiter ces deux méthodes pour résoudre des problèmes de diffraction par des défauts est étudiée. Une approche par éléments finis de frontière basée sur la méthode par ondes partielles est considérée. Elle permet de traiter efficacement le cas de défauts plans. L'extension à des défauts plus généraux est brièvement discutée. / This work adresses the direct problem of the propagation of an elastodynamic field radiated by a source in an anisotropic layered medium. Applications concern non destructive evaluation of composite plates by ultrasonic guided waves. In the lower frequencies, these materials can be modeled as homogeneous, anisotropic and dissipative media. Two causal approaches are studied and developped to solve the wave equation, and their interest is discussed regarding to the widely used harmonic modal method. One of these methods is modal, and is formulated directly in the time domain. It allows to deal easily with anisotropy, even in 3D ; however it also suffers classical shortcomings such as the high cost of the unestablished regime or the difficulty to deal with open waveguides. The other method is a formulation of the so-called partial-waves method in the Laplace domain. Its attractiveness relies in its versatility and in the fact that computational costs can be very acceptable. In a second time, we consider using both methods to solve problems of diffraction by defects. A boundary element method based on the partial-waves approach is developped and leads to solve very efficiently the case of a planar defect. The possibility of treating more general defects is briefly discussed.