In this project, we examine how integration over matrices is performed. We investigate and develop a method for calculating matrix integrals over the set of real square matrices. Matrix integrals are used for calculations in several different areas of physics and mathematics; for example quantum field theory, string theory, quantum chromodynamics, and random matrix theory. Our method consists of ways to apply perturbative Taylor expansions to the matrix integrals, reducing each term of the resulting Taylor series to a combinatorial problem using Wick's theorem, and representing the terms of the Wick sum graphically with the help of Feynman diagrams and fat graphs. We use the method in a few examples that aim to clearly demonstrate how to calculate the matrix integrals. / I detta projekt undersöker vi hur integration över matriser genomförs. Vi undersöker och utvecklar en metod för beräkning av matrisintegraler över mängden av alla reell-värda kvadratiska matriser. Matrisintegraler används för beräkningar i ett flertal olika områden inom fysik och matematik, till exempel kvantfältteori, strängteori, kvantkromodynamik och slumpmatristeori. Vår metod består av sätt att applicera perturbativa Taylorutvecklingar på matrisintegralerna, reducera varje term i den resulterande Taylorserien till ett kombinatoriellt problem med hjälp av Wicks sats, och att representera termerna i Wicksumman grafiskt med hjälp av Feynmandiagram. Vi använder metoden i några exempel som syftar till att klart demonstrera hur beräkningen av matrisintegraler går till.

Data on elastic scattering of 96 MeV neutrons from 56Fe, 89Y and 208Pb in the angular interval 10-70° are presented. The previously published data on 208Pb have been extended, as a new method has been developed to obtain additional information at the most forward angles. The results are compared with phenomenological and microscopic optical potentials. The theory predictions are in general in good agreement with the experimental data. A study of the deviation of the zero-degree cross section from Wick's limit has been performed. The data on 208Pb are in agreement with Wick's limit, while those on lighter nuclei overshoot the limit significantly. A novel analysis method has been developed to obtain the inelastic neutron emission cross sections from the existing 56Fe data. The method is based on folding a trial spectrum with the response of the detector setup. The data cover the angular interval 26-65° and an excitation energy range of 0-45 MeV, ranges hitherto not studied. The results are compared with nuclear model predictions and found to be in good agreement with the experimental data.

Nous nous sommes intéressés à la restauration de la symétrie de réflexion droite-gauche brisée dans certains calculs effectués en utilisant l'approche HTDA (Higher Tamm-Dancoff Approximation). Cette approche a été proposée par le groupe de Bordeaux pour traiter de façon microscopique les corrélations en conservant explicitement les nombres de nucléons. La projection sur la parité par la méthode PAV (projection après variation) utilisant une généralisation du théorème de Wick de type Löwdin s'est avérée être très bien adaptée dans le cadre d'un modèle simplifié pour ce type de calcul et a permis de tourner certaines difficultés propres aux calculs qui utilisent la théorie de la fonctionnelle de la densité déduite par exemple de l'interaction de Skyrme. Les résultats obtenus pour des noyaux lourds manifestant une déformation octupôlaire ou à tout le moins une grande déformabilité pour ce mode, sont en gros tout à fait cohérents avec les calculs antérieurs effectués dans une approche HFB ou HF+BCS. D'autre part nos résultats montrent qu'on peut abaisser par projection sur la parité positive la hauteur de la seconde barrière de fission par une quantité de l'ordre de 1 MeV. / This thesis has been concerned with the restoration of the left-right symmetry broken in some instances. This has been achieved in the framework of the Higher Tamm-Dancoff Approximation (HTDA) proposed by the Bordeaux group to treat correlations in an explicitly particle-number conserving microscopic approach. The parity-projected calculations performed within a PAV (projection after variation) method using a generalized Wick's theorem due to Löwdin has appeared to be a very well-suited frame. It has been implemented within a simple model approach. This has been proposed to clear out some difficulties appearing when one uses an Energy Density Functional approach with an energy density functional issued from an underlying Skyrme interaction. As a result we obtain a fairly good global agreement of our results with previous ones issuing from an HFB approach or its HF+BCS limit, for some heavy nuclei exhibiting a stable octupole deformation or at least a remarkable smoothness for this collective mode. As another result, we have shown that the projection on a positive parity solution is able to reduce the second fission barrier height by about 1 MeV.