De nombreux noyaux atomiques et hypernoyaux se modélisent comme des structures à trois corps. C'est le cas, par exemple, de noyaux à halo, comme 6He, ou de noyaux stables, comme 12C et 9Be. En effet, 6He se caractérise comme un système à trois corps, formé d'un coeur (une particule alpha) et de deux neutrons de valence faiblement liés. Le noyau de 12C peut s'étudier comme un système lié formé de trois particules alphas, tandis que 9Be peut être décrit comme la liaison de deux particules alphas et d'un neutron. Dans les exemples précédents, les particules alphas sont des amas de nucléons. Elles possèdent donc une structure interne dont il faut tenir compte en raison du principe de Pauli. Les modèles les plus réalistes pour décrire les structures à trois corps sont les modèles "microscopiques". Ces modèles prennent en compte explicitement tous les nucléons et respectent exactement le principe d'antisymétrisation de Pauli. Cependant, l'application de ces modèles est fortement limitée en pratique, car ils exigent de trop nombreux et trop longs calculs. Par conséquent, pour simplifier considérablement les calculs et permettre l'étude des structures à trois corps, des modèles moins détaillés, de type "semi-microscopiques", sont également développés. Dans ces modèles, on représente les amas de nucléons comme de simples particules ponctuelles. Dans ce cas, la modélisation consiste à construire les potentiels effectifs entre les amas, puis à les employer dans les modèles à trois corps. Dans ce travail, nous avons développé les modèles "semi-microscopiques à trois corps". Les potentiels effectifs entre amas sont directement déduits des forces entre nucléons (selon la RGM à 2 corps). Ces potentiels sont "non-locaux", et dépendent des énergies des amas qui interagissent. Ils permettent de simuler le principe de Pauli et les échanges de nucléons entre les amas. La dépendance en l'énergie se révèle être un inconvénient dans les modèles à trois corps. Les potentiels effectifs sont par conséquent transformés en de nouveaux potentiels (non-locaux) indépendants de l'énergie, bien adaptés aux modèles à trois corps. Les modèles "semi-microscopiques" sont beaucoup plus simples et plus rapides que les modèles "microscopiques". Ils fournissent les fonctions d'onde des états liés à trois corps des noyaux légers et hypernoyaux. Cela permet d'une part de comprendre les propriétés spectroscopiques nucléaires, et d'autre part, cela ouvre la voie pour de futurs modèles de réactions nucléaires impliquant les structures à trois corps. / Several atomic nuclei and hypernuclei can be modelled as three-body structures: e.g., two-neutron halo nuclei, such as 6He, and other nuclei, such as 12C and 9Be. Indeed 6He can be represented as a three-body system, made up of a core (an alpha particle) and two weakly bound valence neutrons. The 12C nucleus can be studied as a bound system formed by three alpha particles, while the 9Be nucleus can be described as the binding of two alpha particles and one neutron. In these typical examples, the alpha particles are clusters of nucleons. They have an internal structure that must be taken into account because of the Pauli principle. The most realistic models are the "microscopic models". In these models, all the nucleons are taken into account, and the Pauli antisymmetrisation principle is fully respected. However, the application of the "microscopic models" is limited in practice, because they require too many laborious calculations. Therefore, in order to greatly simplify the calculations, "semi-microscopic models" are developed. In those models, the clusters of nucleons are treated as ("structureless") pointlike particles. The models then consist in determining the effective potentials between the clusters, and in using them in three-body models. In the present work, we have developed "semi-microscopic models". The effective potentials between the clusters are directly obtained from the interactions between nucleons (according to the two-cluster RGM). These potentials are "nonlocal", and depend on the energy of the interacting clusters. The non-locality is a direct consequence of the Pauli principle and the exchanges of nucleons between the clusters. The energy-dependence of the potentials turns out to be a drawback in three-body models. Therefore, the effective potentials are transformed into energy-independent potentials, which can be used in three-body models. The "semi-microscopic models" are much simpler and faster than the "microscopic models". They provide the three-body bound-state wave functions (i.e., the spectroscopic properties and the structure) of light nuclei and hypernuclei. Such wave functions are also the basic ingredient that will be used in future reactions models.

The double hypernuclear systems are studied within the context of the hyperspherical approach. Possible bound states of these systems are sought as zeros of the corresponding three-body Jost function in the complex energy plane. Hypercentral potentials for the system are constructed from known potentials in order to determine bound states of the system. Calculated binding energies for double- hypernuclei having A = 4 − 20, are presented. / Physics / M.Sc. (Physics)

A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods. / Physics

The double hypernuclear systems are studied within the context of the hyperspherical approach. Possible bound states of these systems are sought as zeros of the corresponding three-body Jost function in the complex energy plane. Hypercentral potentials for the system are constructed from known potentials in order to determine bound states of the system. Calculated binding energies for double- hypernuclei having A = 4 − 20, are presented. / Physics / M.Sc. (Physics)

A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods. / Physics / M.Sc. (Physics)

Nuclear electromagnetic breakup processes at low energy are particularly relevant in the astrophysical context. In this Thesis we analyse the Beryllium-9 photodisintegration reaction, whose inverse process, under certain astrophysical conditions, is related to the Carbon-12 formation. A preliminary study of the Carbon-12 photodisintegration is also carried out. The interaction of these nuclei with a low-energy photon induces a transition to a state consisting of cluster sub-units, the alpha-particles, and possibly a neutron, n. The theoretical study of the cross section in the low-energy regime is conducted by using a three-body ab initio approach. Beryllium-9 exhibits a clear separation of energy scales, since its alpha-alpha-n three-body binding energy is shallow compared to the binding of the alpha-particle. Within this framework a halo/cluster Effective Field Theory (EFT) can be developed. The alpha-alpha and alpha-n effective interactions are defined in momentum space as a series of contact terms, regularized by a momentum-regulator function. The Low Energy Constants are expressed in terms of scattering observables, i.e. scattering length and effective range. A three-body potential is also introduced in the model. Carbon-12 is studied on the same footing. By means of an integral transform approach, the problem of the transition to a state in the continuum can be advantageously reformulated in terms of a bound-state problem: in the calculations we use the Lorentz Integral Transform method, in conjunction with the Non-Symmetrized Hyperspherical Harmonics method. In determining the low-energy photodisintegration cross section, the nuclear current matrix element is evaluated through the electric dipole, or quadrupole, transition operator (Siegert theorem). Since the continuity equation is used explicitly, the contribution of the one-body and the many-body current operators is implicitly included in the calculation. By comparing the results with those obtained by using a one-body convection current, the effect of the many-body terms can be quantified. The dependence of the results on different EFT parameters is discussed, always in connection with the experimental data available in the literature. By following the power counting dictated by the EFT approach for Beryllium-9, the inclusion of different partial waves in the potential model is explored. In addition to a alpha-alpha S-wave, a alpha-n P-wave and a three-body effective interaction, a alpha-n S-wave term is also required to obtain results more consistent with the experimental data. The contribution of the many-body currents to the cross section is found to be non-negligible. Although at an early stage, Carbon-12 results show interesting features. The formalism presented in this Thesis can be extended to study the photodisintegration of Oxygen-16 within a fully four-body ab initio approach.

De nombreux noyaux atomiques et hypernoyaux se modélisent comme des structures à trois corps. C'est le cas, par exemple, de noyaux à halo, comme 6He, ou de noyaux stables, comme 12C et 9Be. <p>En effet, 6He se caractérise comme un système à trois corps, formé d'un coeur (une particule alpha) et de deux neutrons de valence faiblement liés. Le noyau de 12C peut s'étudier comme un système lié formé de trois particules alphas, tandis que 9Be peut être décrit comme la liaison de deux particules alphas et d'un neutron.<p><p>Dans les exemples précédents, les particules alphas sont des amas de nucléons. Elles possèdent donc une structure interne dont il faut tenir compte en raison du principe de Pauli.<p><p>Les modèles les plus réalistes pour décrire les structures à trois corps sont les modèles "microscopiques". Ces modèles prennent en compte explicitement tous les nucléons et respectent exactement le principe d'antisymétrisation de Pauli. Cependant, l'application de ces modèles est fortement limitée en pratique, car ils exigent de trop nombreux et trop longs calculs.<p>Par conséquent, pour simplifier considérablement les calculs et permettre l'étude des structures à trois corps, des modèles moins détaillés, de type "semi-microscopiques", sont également développés. Dans ces modèles, on représente les amas de nucléons comme de simples particules ponctuelles. Dans ce cas, la modélisation consiste à construire les potentiels effectifs entre les amas, puis à les employer dans les modèles à trois corps.<p><p>Dans ce travail, nous avons développé les modèles "semi-microscopiques à trois corps". Les potentiels effectifs entre amas sont directement déduits des forces entre nucléons (selon la RGM à 2 corps). Ces potentiels sont "non-locaux", et dépendent des énergies des amas qui interagissent. Ils permettent de simuler le principe de Pauli et les échanges de nucléons entre les amas. La dépendance en l'énergie se révèle être un inconvénient dans les modèles à trois corps. Les potentiels effectifs sont par conséquent transformés en de nouveaux potentiels (non-locaux) indépendants de l'énergie, bien adaptés aux modèles à trois corps. Les modèles "semi-microscopiques" sont beaucoup plus simples et plus rapides que les modèles "microscopiques". Ils fournissent les fonctions d'onde des états liés à trois corps des noyaux légers et hypernoyaux. Cela permet d'une part de comprendre les propriétés spectroscopiques nucléaires, et d'autre part, cela ouvre la voie pour de futurs modèles de réactions nucléaires impliquant les structures à trois corps.<p><p>/<p><p>Several atomic nuclei and hypernuclei can be modelled as three-body structures: e.g. two-neutron halo nuclei, such as 6He, and other nuclei, such as 12C and 9Be.<p>Indeed 6He can be represented as a three-body system, made up of a core (an alpha particle) and two weakly bound valence neutrons. The 12C nucleus can be studied as a bound system formed by three alpha particles, while the 9Be nucleus can be described as the binding of two alpha particles and one neutron.<p><p>In these typical examples, the alpha particles are clusters of nucleons. They have an internal structure that must be taken into account because of the Pauli principle.<p><p>The most realistic models are the "microscopic models". In these models, all the nucleons are taken into account, and the Pauli antisymmetrisation principle is fully respected. However, the application of the "microscopic models" is limited in practice, because they require too many laborious calculations.<p>Therefore, in order to greatly simplify the calculations, "semi-microscopic models" are developed. In those models, the clusters of nucleons are treated as ("structureless") pointlike particles. The models then consist in determining the effective potentials between the clusters, and in using them in three-body models.<p><p>In the present work, we have developed "semi-microscopic models". The effective potentials between the clusters are directly obtained from the interactions between nucleons (according to the two-cluster RGM). These potentials are "nonlocal", and depend on the energy of the interacting clusters. The non-locality is a direct consequence of the Pauli principle and the exchanges of nucleons between the clusters. The energy-dependence of the potentials turns out to be a drawback in three-body models. Therefore, the effective potentials are transformed into energy-independent potentials, which can be used in three-body models. The "semi-microscopic models" are much simpler and faster than the "microscopic models". They provide the three-body bound-state wave functions (i.e. the spectroscopic properties and the structure) of light nuclei and hypernuclei. Such wave functions are also the basic ingredient that will be used in future reactions models. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished