In this work we calculate the binding energies and root-mean-square radii for A−body nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic potentials. The equations are solved numerically. For this purpose, the equations are transformed into an eigenvalue equation via the orthogonal collocation procedure using triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined. For A > 3, the Potential Harmonic Expansion Method is employed. Using this method, the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike amplitudes are expanded on the potential harmonic basis. To transform the resulting coupled differential equations into an eigenvalue equation, we employ again the orthogonal collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O and 40Ca. / Physics / M. Sc. (Physics)

L'analyse des conditions physico-chimiques régnant dans le milieu interstellaire(ISM) nécessité de connaître les constantes de vitesse de collision inélastique qui ont lieu plus fréquemment dans l'ISM. Nous avons à cettefin calculées les surfaces d'énergie potentielles ainsi que les états liés descomplexes CS-H2, HCN-H2, HCN-He et C3-He. Nous avons déterminé pour la collision CS-H2 les sections efficaces et les taux d'excitation collisionnels pour les premiers niveaux rotationnels. Des observations récentes suggérentque l'excitation des modes de pliage des molécules triatomiques doit êtreprise en compte dans les modèles astrochimiques. Nous présentons doncdeux nouvelles approches théoriques permettant d'effectuer un traitementClose Coupling des collisions inélastiques d'un atome avec une molécule triatomique. Le couplage entre les mouvements de rotation et de pliage de la molécule est traité soit exactement dans le cadre de l'approximation du rigid bender (RBCC) ou de façon approximée en moyennant le potentiel d'interaction atome-molècule sur le mode de pliage de la molécule (RBAA). La méthode RBCC est appliquée à l'étude des collisions HCN-He et C3-He pour lesquelles les sections efficaces de transition entre niveaux rotationnels appartenant à des modes de pliage différents sont obtenues. Les résultats sont comparés avec ceux fournis par l'opproximation du rotateur rigide linéaire. Dans le cas de la collision HCN-He ils sont aussi comparés avec ceux obtenus en utilisant l'approche RBAA. Nous montrons que les sections efficaces de transitions entre des niveaux rotationels appartenant à des niveaux de bending différents doivent être calculées au niveau RBCC. / Tha analysis of the physico-chemical conditons taking place in the interstellar medium (ISM) requires to know the inclastic rate coefficents of the detected interstellar molecules in collisions with the moste common colliders int the ISM. We have comuted the four dimensional potential energy surfaces, and the bound levels for the CS-H2, HCN-H2, HCN-He and C3 -He complexes. For the collisions of Cs with H2, we also determined the rst inelastic cross section and rate coefficeients<; Several recent observations suggest that the vibrational excitation of triatomic molecules in the ISM at least in the bending motion needs to be considered in the collision mechanismes. We present a nex theorical method to treat atom-rigid bender ineslastic collisions at close the coupling level (RBCC). The coupling between rotation and bending is treated exactly within the rigid bender approximation and we obtain the cross section for the rotational transition between levels belonging to dierent bending levels. This approach is applied to the study of HCN-He and C3-He. The results are compared with those obtained whenconsidering the molecules to be linear rigid rotors. In the case of HCN-He,they are also compared with the cross sections determined using the interactionpotential averaged over the bending wavefunction. We demonstratethat the cross sections involving vibrational transitions should be computedusing the RBCC method. For HCN-He, the linear rigid approach is foundto offer a good description of pure rotational transitions while for C3-Hethis method is shown to overestimate the cross section for collision energieshigher than the first excited bending threshold.

Cette thèse porte sur le calcul des états liés et de diffusion de systèmes à deux corps dans une formulation explicitement covariante de la dynamique sur le front de lumière. Nous traitons dans ce cadre deux particules scalaires en interaction à l'approximation "ladder" (modèle de Wick-Cutkosky massif). Les états liés sont calculés (onde S et P) par une décomposition angulaire du potentiel. Nous montrons que la restriction de cette décomposition à sa première composante suffit pour décrire correctement le système, ce qui revient à approximer le potentiel par sa moyenne sur toutes les directions du front de lumière. Ce résultat facilite le traitement des états de diffusion. Nous calculons donc des déphasages élastiques (onde S et P). Or notre potentiel relativiste prend en compte l'ouverture d'un canal inélastique au-delà du seuil de création. Nous calculons donc des déphasages correspondant à l'émision d'un boson, qui violent cependant l'unitarité de la matrice S. La prise en compte la self-énergie permet de résoudre ce problème comme nous montrons par un calcul perturbatif. L'ajout de la self-énergie permet d'obtenir des déphasages inélastique respectant l'unitarité de S. Nous montrons aussi que la self-énergie modifie considérablement les conditions d'existence d'états liés. Nous considérons aussi le cas des deux fermions en interaction par un échange scalaire ou pseudo-scalaire (état $J^\pi=0^+$). Les états liés sont traités par une décomposition angulaire, mais la propriété de moyenne n'apparaît pas pour le couplage pseudo-scalaire. Elle apparaît pour le couplage scalaire, ce qui nous permet de calculer des déphasages élastiques et inélastiques à l'approximation ladder. Abstract : This thesis concerns the two-body scattering and bound states in an explicitly covariant formulation of the light-front dynamics. We consider, in this framework, two scalar particles in interaction at the "ladder" approximation (massive Wick-Cutkosky model). S and P-waves bound states are calculated by an angular decomposition of the potential. We show that the first term of the decomposition gives already a very good description of the system, what is equivalent to take an averaged potential over the light-front directions. This results simplifies the treatment of the scattering states. We obtain the elastics phase shifts (S and P waves). Yet our relativistic potential take into account the first inelastic threshold, what corresponds to the one boson emission. These phase shifts do not respects the S-matrix unitarity. We show by a perturbative calculation that the addition of self-energy contributions permits to solve this problem. Adding this term, allows to obtain an inelastic phase-shift respecting S-matrix unitarity. We show also that the self-energy contribution strongly modifies the conditions of existence of a bound state. We consider also two fermions interacting by a scalar or pseudoscalar exchange ($J^\pi=0^+$ state). The bound states are calculated by the angular decomposition method, that works well here but fails in the pseudoscalar coupling. The average method is finally used to calculate the scattering states in the ladder approximation fo the scalar coupling.

In this work we calculate the binding energies and root-mean-square radii for A−body nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic potentials. The equations are solved numerically. For this purpose, the equations are transformed into an eigenvalue equation via the orthogonal collocation procedure using triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined. For A > 3, the Potential Harmonic Expansion Method is employed. Using this method, the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike amplitudes are expanded on the potential harmonic basis. To transform the resulting coupled differential equations into an eigenvalue equation, we employ again the orthogonal collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O and 40Ca. / Physics / M. Sc. (Physics)

<p>    </p> <p>We live in an age in which computation touches upon every aspect of our lives in ever increasing ways. To meet the demand for increased computing power and ability, new computation strategies are continually being proposed. In this dissertation, we consider two research projects related to two such cutting edge paradigms. We first consider developing superconducting devices that implement asynchronous reversible ballistic computation. This paradigm was developed to circumvent Landauer’s principle of a minimum energy required per bitwise computation operation. We report the design of a new device, the rotary, which is a critical step towards developing universal computation gates in the scheme of synchronous reversible ballistic computation. Next, we turn to the consideration of anyons which have been predicted to enable topological quantum computing, a quantum computing paradigm that is relatively immune to environmental noise. We consider initial steps in the development of a Bethe ansatz solvable model that will help decipher the many-body properties of Majorana zero modes in superconducting Kitaev wires. </p>