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International audience; The single-particle states are degenerate in the ground-state of an even-even nucleus since there are at least two states (corresponding to spin up and spin down) with the same energy. However, this is not the case for odd-mass nucleus due to the existence of the unpaired nucleon which breaks the time reversal symmetry. The impact of the time-reversal symmetry breaking on a wide range of rare earth nuclei has been investigated recently within the Skyrme mean-field approach using the Skyrme SIII parametrization [1]. In order to have a more complete assessment on the impact of time-reversal symmetry breaking on nuclear properties, we performed calculations using the SLy5* parametrization with BCS pairing. The seniority force is used to approximate the residual pairing interaction. In this work, some nuclear properties of odd-mass rare earth nuclei namely binding energy, nuclear charge radii, spectroscopic charge quadrupole moment and band-head energy spectra are compared to previous SIII calculations and experimental data.

International audience; Nuclear structure data plays an important role in nuclear physics studies and applications such as nuclear power generation. This article presents evaluations of a mean-field approach to describe two nuclear structure quantities namely the electric and magnetic moments. The Hartree-Fock-plus-pairing approach was employed with pairing correlations treated within the Bardeen-Cooper-Schrieffer (BCS) framework. The Skyrme SIII parametrization and seniority force are chosen to approximate the effective nucleon-nucleon and pairing interactions, respectively. Calculated results show that the self-consistent blocking procedure which takes into account time-reversal symmetry breaking is important to reproduce experimental magnetic moment

The addition of an extra nucleon to an even-even core generates, in most cases, a polarization of this core which is essentially due to a spin paramagnetic type of coupling. It is shown here that these results (which have been obtained so far only with the SIII Skyrme force) seems to be robust against the change of the Skyrme force parameters for the charge state corresponding to the added nucleon and somewhat less for the other charge state. The consequences drawn from calculations with the SIII force about the effect of the core polarization on the effective spin gyromagnetic factors, hold also for the two other Skyrme force parametrizations (SkM* and SLy4) considered here. A very good reproduction of the average phenomenological quenching of these factors from their free values, is also obtained. Finally, the rare cases where these rules do not hold are discussed.

International audience; We present a formalism to study the isospin content of a nuclear state in the framework of the Higher Tamm-Dancoff Approximation. This formalism is then applied to the description of even-even N = Z nuclei. Finally a schematic two-level model provides some insight into the isospin-mixing mechanism at work and the impact of the pairing correlations on the isospin-mixing parameter.

In four well-deformed heavy odd nuclei, the energies of low-lying rotational band heads have been determined microscopically within a self-consistent Hartree-Fock-plus-BCS approach with blocking. A Skyrme nucleon-nucleon effective interaction has been used together with a seniority force to describe pairing correlations. Only such states which are phenomenologically deemed to be related to single-particle excitations have been considered. The polarization effects, including those associated with the genuine time-reversal symmetry breaking have been fully taken into account within our model assumptions. The calculated spectra are in reasonably good qualitative agreement with available data for the considered odd-neutron nuclei. This is not so much the case for the odd-proton nuclei. A potential explanation for such a difference in behavior is proposed.

Super-allowed 0+ → 0+ Fermi transitions provide a test at low energy of the Standard Model of elementary interactions. The isospin-symmetry breaking due to the electromagnetic interaction at a nuclear level is a fundamental theoretical tool for the understanding of weak processes beyond the Standard Model. Within the Higher Tamm–Dancoff description of correlated nuclear states, we calculate the isospin-symmetry breaking correction δc to the Fermi transition matrix element. A sensitivity study on the T = 0 pairing correlations is carried out and some tests of model ingredients are performed. The obtained correction is of the order of 0.15~0.2% for plausible strengths in the T = 1 and T = 0 channels of the residual interaction. This is expected to constitute a lower bound.

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

In the framework of the Higher Tamm-Dancoff Approximation which allows for a consistent treatment of pairing and quadrupole vibrational correlations preserving the particle-number symmetry and the Pauli principle, we compare the isospin content of ground and excited Kπ = 0+ states including either type of the above mentioned correlations using an approximate projection-after-variation technique for isospin. The pairing correlations are described with a delta interaction using the same strength in the T = 0 and T = 1 channels, whereas the vibrational correlations are treated with an isoscalar quadrupole-quadrupole interaction. As a first study, we apply this approach in the N = Z, even-even 16 O nucleus. For the same amount of correlations measured by the diffusivity of Fermi surface or depletion of particle-hole vacuum in the ground-state solution, we find very similar isospin mixing in the ground state for both types of correlations, but different patterns for the distribution in the calculated solutions of the expectation value of the square of the isospin operator.

An introduction of the different quantum mechanics models is given for the calculation of pre‐equilibrium multistep direct process for nucleon induced reaction. A practical application is presented for 238U neutron induced reaction at medium energy (10–20 MeV). The double differential cross‐sections are calculated with no adjustable parameter and reproduced the data very well. The cross‐sections are expressed as a sum of DWBA transition amplitudes computed with a microscopic two‐body interaction. The exited states of the target are expressed as particle‐hole excitations built from single particle states obtained with the HF+BCS calculation with a Skyrme force. We also perform a sensitivity study our calculations with respect to the ingredients of the model, namely the two‐body interaction which generates the transitions and the target states description.

International audience; We present the key aspects of the theoretical foundations of the Higher Tamm–Dancoff Approximation which can be interpreted as a truncated shell-model approach based on a Hartree–Fock solution, ensuring the conservation of the particle number. Then we discuss some phenomenological aspects of the residual interactions used, namely the delta interaction to describe the neutron–neutron and proton–proton pairing correlations and the quadrupole–quadrupole interaction to describe vibrational correlations.

Preequilibrium multistep direct (MSD) double differential cross sections are calculated for medium energy inelastic neutron scattering (11-18MeV) on 208 Pb and 238 U. A microscopic approach is used, since no adjustable parameters are involved. Cross section are expressed as a sum of DWBA transition amplitudes computed with the microscopic two-body interaction M3Y. Final target states are expressed as particle-hole excitations built from single particle states obtained within the HF+BCS theory applied with Skyrme force.

In this work, we are interested in the treatment of odd-mass atomic nuclei in energydensity functional (EDF) models. More precisely, the goal of this thesis is to develop and to applyto odd-mass nuclei, the theoretical extensions of the EDF method that are: (i) the projectiontehnique, and (ii) the configuration mixing by the generator coordinate method (GCM). Thesetwo extensions are part of the so-called multi-reference energy density functional (MR-EDF)formalism and allow for taking into account, within an EDF context, the "beyond-mean-field"correlations between the nucleons forming the nucleus. Until now, the MR-EDF formalism hasbeen applied, in its full-fledged version, only to the calculation of even-even nuclei. In this thesis,we want to demonstrate the applicability of such a model also for the description of odd-massnuclei. In the first part of this thesis, we describe the theoretical formalism of the EDF models,giving particular attention to the treatment of symmetries within our approach. In the secondpart of the manuscript, we apply our model to the nucleus 25Mg and investigate different aspectsof the method (e.g. numerical accuracy, convergence of the configuration mixing, comparison toknown experimental data). The results obtained in this work are encouraging and demonstratethe potential of our approach for theoretical nuclear structure calculations., Dans ce manuscrit de thèse, nous nous intéressons à la description des noyaux atomiques composés d’un nombre impair de nucléons dans la méthode dite de la fonctionnelle énergiede la densité (EDF). Plus précisément, nous présentons et appliquons dans le cas de ces noyaux,des extensions à cette méthode : (i) la projection sur les bons nombres quantiques, (ii) le mélange de configurations à travers la méthode des coordonnées génératrices (GCM), qui permettent deprendre en compte dans nos calculs des corrélations de type « au-delà du champ moyen » entre les nucléons constituant le noyau. De telles extensions n’avaient jusqu’alors été employées, dansleurs versions les plus générales, qu’aux noyaux ayant à la fois un nombre pair de neutrons etde protons, et nous nous proposons donc de démontrer leurs applicabilités également dans le cas des noyaux impairs. Dans la première partie de ce travail, nous présentons le formalisme mathématique de la méthode EDF, en mettant tout particulièrement l’accent sur le traitement des symétries dans cette approche. Dans la seconde partie du manuscrit, nous appliquons notre modèle au cas du noyau de 25Mg et analysons les résultats sous différents angles (ex : précision numérique des résultats, convergence du mélange de configurations, comparaison avec les données expérimentales connues). Les premiers résultats obtenus dans ce travail de thèse sontencourageants et démontrent l’intérêt de notre approche pour les calculs théoriques de structure nucléaire.

In this work, we have developed the Hartree-Fock (HF) approximation in momentum space for deformed nuclei with a general nucleon-nucleon (NN) potential. The structure of such a potential has been investigated in momentum space from its symmetries. Its constructions has been realized in a tensorial separable momentum-spin-isospin representation. Moreover, to treat low-momentum interactions, we have implemented the Similarity Renormalization Group approach. Three momentum representations have been studied: the plane-wave, the partial-wave and the confined plane-wave. The numerical implementation has been validated against an existing HF-Skyrme code in the harmonic oscillator basis. We have found that the confined plane-wave basis provides many advantages over the two others, namely: flexible construction of symmetry-adapted bases, efficient calculation of matrix elements (nuclear, Coulomb and center of mass kinetic correction) and optimization in ressources (time and memory). This basis is characterized by two parameters: the confinement box size (cube) which can be essentially related to the nuclear radius and a single-particle momentum cut-off which is directly linked to the cut-off in relative momentum of the interaction. Bulk properties of some spherical and deformed even-even nuclei in the mass region A < 100 have been calculated with recently developed NN potentials. The resulting residual interaction has been derived to study pairing correlations within the Highly Truncated Diagonalization Approach (HTDA). In particular, the question of the convergence with the model space has been addressed., Dans ce travail, nous avons étudié l'approximation Hartree-Fock (HF) dans l'espace implusion de façon adaptée à la description des noyaux déformés avec un potentiel nucléon-nucléon (NN) général. La structure d'un tel potentiel a été étudiée à partir de ses symétries et sa construction a été réalisée dans une représentation tensorielle séparable des opérateurs d'impulsion-spin-isospin. En plus, pour traiter des interactions à basse impulsion, nous avons également mis en oeuvre l'approche du groupe de renormalisation par transformation de similarité du potentiel NN. Plusieurs représentations en impulsion ont été étudiées: l'onde plane, l'onde partielle et l'onde plane confinée. L'implémentation numérique de l'approche HF a été validée par comparaison avec un code HF-Skyrme en base d'oscillateur harmonique. Nous avons trouvé que la base d'onde plane confinée offre le plus d'avantages: flexibilité dans le choix du groupe de symétrie auto-cohérente, facilité dans le calcul des éléments de matrice de l'interaction (nucléaire, Coulombienne et la correction cinétique du centre de masse), optimisation des ressources (temps et mémoire). Elle fait intervenir deux paramètres : la taille de boîte de confinement (cube) et la coupure sur l'impulsion individuelle. Nous avons montré que cette coupure a un lien direct avec la coupure d'impulsion de l'interaction et que la taille de boîte est essentiellement liée à celle du noyau. Des calculs de propriétés globales du noyau ont été effectués dans des noyaux magiques et déformés dans le région de masse A < 100 avec divers potentiels récemment dévéloppés. A partir de la solution HF obtenue, les corrélations d'appariement ont été étudiées avec l'interaction résiduelle issue du potentiel NN dans le formalisme HTDA (Highly Truncated Diagonalization Approach). En particulier, la question de la convergence en fonction de l'espace du modèle a été abordée.

While there have been numerous microscopic calculations on fission barriers of even-even compoundnuclei, there are however, relatively few such work dedicated to odd-mass nuclei. This is dueto the complications posed by the breaking of the time-reversal symmetry at the mean-field leveldue to the presence of an unpaired nucleon. In order to circumvent this difficulty, previous fission barriercalculations of odd-mass nuclei have been performed by neglecting the effect of time-reversalsymmetry breaking. This work aims to improve on the description of fission barriers as well asthe spectroscopic properties of ground and fission-isomeric state, of some odd-mass actinide nucleiby taking the effect of time-reversal symmetry breaking into account. This has been perfomedwithin a Skyrme-Hartree-Fock-plus-BCS framework with blocking, where the BCS formalism hasbeen adapted to accomodate this symmetry breaking. The Skyrme nucleon-nucleon effective forcehas been used with various sets of parameters (SIII, SkM*, SLy5*). The residual pairing interactionhas been approximated by seniority forces whose neutron and proton parameters have beenfitted to reproduce the odd-even mass differences of some actinide nuclei. The low-lying rotationalband-head energies evaluated within the Bohr-Mottelson unified model have been determined forfour well-deformed odd-nuclei (235U, 239Pu, 237Np, 241Am) yielding a good qualitative agreementto the data for odd-neutron nuclei. The agreement was significantly less good for the odd-protonnuclei, possibly due to the use of the Slater approximation for the exchange Coulomb interaction.The deformation energies of two odd-neutron nuclei (235U and 239Pu) have been calculated forsome single-particle configurations up to a point beyond the outer fission-barrier. Axial symmetrynuclear shape has been assumed while a breaking of the left-right (or intrinsic parity) symmetryhas been allowed around the outer fission-barrier. The fission-barrier heights of such odd-neutronnuclei depend significantly on the particle configurations. A special attention has been paid tothe very important rotational correction to deformation energies. In particular, the correction ofthe moment of inertia calculated from the usual Belyaev expression was considered. Overall, aqualitative agreement with available data on fission-barrier heights for the considered odd-neutronnuclei and their even neighbours has been obtained., Alors qu’il existe de nombreux calculs microscopiques de barrières de fission pour des noyaux composés pair-pairs, il n’y a cependant que relativement peu de tels calculs pour des noyaux de masse impaire. Ceci est dû aux complications induites par la brisure de la symétric de reversement du sens du temps au niveau du champ moyen qui est engendrée par la présence d’un nucleon non apparié. Pour éviter cette difficulté, des calculs existants pour des noyaux de masse impaire ont tout simplement négligé ces effets de brisure de la symétrie de reversement du sens du temps.Dans ce travail, on se donne pour but d’améliorer la description des barrières de fission, aussi bien que des propriétés spectroscopiques du niveau fondamental et de l’état isomérique de fission,pour quelques isotopes de masse impaire dans la région des actinides en prenant en compte de tels effets. Ceci a été réalisé dans le cadre du formalisme de Skyrme–Hartree–Fock plus BCS avec blocking en adaptant ce formalisme à la brisure de la symétrie considérée. L’interaction résiduelle d’appariement a été approchée par une force de séniorité dont les paramètres ont été ajustés pour reproduire les différences de masse pair-impair de quelques noyaux de la région des actinides.Les énergies des têtes de bande rotationnelle de basse énergie ont été calculées dans le cadre du modèle unifié de Bohr-Mottelson pour quatre noyaux bien déformés (235U, 239Pu, 237Np, 241Am)produisant un bon accord qualitatif avec les données pour les noyaux impairs en neutrons. L’accord significativement moins bon obtenu pour les noyaux impairs en protons pourrait résulter de l’usage de l’approximation de Slater pour l’interaction d’échange de Coulomb. Les énergies de déformation de deux noyaux impairs en neutrons (235U, 239Pu) ont été calculées pour quelques configurations de particule individuelle, jusqu’après la barrières de fission externe. La symétrie axiale a été imposée tandis que la brisure de la symétrie droite-gauche (ou de parité intrinsèque) a été permise dans la région de la seconde barrière. Les hauteurs des barrières de fission pour ces noyaux impairs dépendent significativement des configurations de particule individuelle. Un accord qualitatif avec les données disponibles pour les hauteurs de barrières des noyaux impairs considérés et leurs voisins pair-pairs a été généralement obtenu.