The rapid neutron-capture process, known as the r-process, is responsible for the origin of about half the stable nuclei heavier than iron observed in nature. Though the r-process is believed to take place in explosive stellar environments and to involve a large number (few thousands) of exotic nuclei, this nucleosynthesis process remains poorly understood from the astrophysics as well as nuclear physics points of view. On the nuclear physics side, the nuclei are too exotic to be studied in the laboratory, even though great efforts are constantly made to extend the experimental limits away from the eta-$stability region. Therefore, theoretical models are indispensable to estimate the nuclear properties of interest in the r-process nucleosynthesis modelling. So far, models used to predict the properties of the exotic nuclei were based on parametrized macroscopic-type approaches the reliability of which is questionable when extrapolating far away from the experimentally known region. This work is devoted to the improvement of nuclear predictions, such as the nuclear ground- and excited-state properties, needed as input data to model the r-process. In order to give the predictions a reliable character, we rely on the microscopic mean-field Hartree-Fock theory based on the Skyrme-type interaction. Pairing correlations play an important role in the description of nuclei, and become essential for nuclei located near the drip lines, since the scattering of pairs of quasi-particles into the continuum increases significantly. In this work, we brought to the Hartree-Fock model the self-consistent treatment of the pairing correlations within the Hartree-Fock-Bogoliubov (HFB) theory. Further improvements are made in the restoration of symmetries broken by correlations added in the form of additional degrees of freedom in the wave function. These include the translational invariance restored by calculating the recoil energy, the particle-number symmetry by an exact projection after variation, the rotational symmetry by an approximate cranking correction and the parity symmetry for reflection asymmetric shapes. In addition, the renormalization of the HFB equations has been studied as well and allows to eliminate the dependence of the total energy with respect to the cutoff energy. The effective nucleon-nucleon interaction is determined by adjusting its parameters on all available experimental masses, with some constraints derived from fundamental nuclear matter properties. A systematic study of the influence on mass predictions for each of the above cited improvements as well as of some uncertainties affecting the particle-hole and particle-particle interactions has been conducted. In spite of quite important differences in the input physics, we find a great stability in the mass predictions for exotic neutron-rich nuclei, though local mass differences can be significant. Each of the Skyrme force derived in the present work has been tested on the predictions of basic ground-state properties (including charge radii, quadrupole moments, single-particle levels), fission barriers and electric dipole $gamma-$ray strengths. The HFB predictions globally reproduce experimental data with a level of accuracy comparable with the widely-used droplet-like models. The microscopic character of the approach followed in the present work makes however the predictions for exotic neutron-rich nuclei involved in the r-process more reliable. The influence of such improved nuclear mass predictions on the r-process abundance distribution is studied in the specific scenario of the prompt supernova explosion mechanism.

Les travaux présentés visent à améliorer les modèles de physique nucléaireutilisés dans l’évaluation des sections efficaces neutroniques de fission. Le résultat deces travaux donne les clefs pour une percée significative dans ce domaine et a permisd’étendre fortement les capacités du code d’évaluation CONRAD. Les sections partiellesétant naturellement corrélées entre-elles pour respecter la valeur de la section totale, cesaméliorations bénéficient à l’ensemble des sections partielles. Un cadre solide pour lamodélisation des processus concurrent à la fission a dû être établi sur le modèle du codede référence TALYS. Après s’être assuré de la fiabilité et de la cohérence du cadre, lesinvestigations spécifiques concernant la fission ont pu être réalisées. Les perspectivesd’applications offertes par les modèles macro-microscopiques FRDM et FRLDM ont étéanalysées. Ces modèles ont été implémentés et validés sur des données expérimentaleset des benchmarks. Afin d’obtenir des temps de calcul compatibles avec les besoins del’évaluation, des méthodes numériques sophistiquées ont été sélectionnées et une partiedes calculs a été portée sur GPU. Ces modèles macro-microscopiques peuvent être utiliséspour construire des surfaces d’énergie potentielle qui sont à leur tour traitées afin d’obtenirdes barrières de fission à une dimension, puis des coefficients de transmission fission. Cesderniers sont alors utilisés dans le cadre de modélisation des sections efficaces moyennesdu domaine statistique sur la base d’un modèle Hauser-Feshbach. Les résultats de cetteapproche seront présentés sur le cas du 239Pu(n,f). / The work presented here aims to improve models used in the fission crosssectionevaluation. The results give insights for a significant breakthrough in this fieldand yielded large extensions of the evaluation code CONRAD. Partial cross sections areinherently strongly correlated together as of the competition of the related reactions mustyield the total cross section. Therefore improving fission cross section benefits to all partialcross sections. A sound framework for the simulation of competitive reactions hadto be settled in order to further investigate on the fission reaction; this was implementedusing the TALYS reference code as guideline. After ensuring consistency and consistencyof the framework, focus was made on fission. Perspective resulting from the useof macroscopic-microscopic models such as the FRDM and FRLDM were analyzed; thesemodels have been implemented and validated on experimental data and benchmarks. Tocomply with evaluation requirements in terms of computation time, several specific numericalmethods have been used and parts of the program were written to run on GPU.These macroscopic-microscopic models yield potential energy surfaces that can be used toextract a one-dimensional fission barrier. This latter can then be used to obtained fissiontransmission coefficients that can be used in a Hauser-Feshbach model. This method hasbeen finally tested for the calculation of the average fission cross section for 239Pu(n,f).

Doctorat en sciences, Spécialisation physique / info:eu-repo/semantics/nonPublished

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.