Bound state systems consisting of three nonrelativistic particles are numerically studied. Calculations are performed employing two-body and three-body forces as input in the Hamiltonian in order to study the role or contribution of three-body forces to the binding in these systems. The resulting differential Faddeev equations are solved as three-dimensional equations in the two Jacobi coordinates and the angle between them, as opposed to the usual partial wave expansion approach. By expanding the wave function as a sum of the products of spline functions in each of the three coordinates, and using the orthogonal collocation procedure, the equations are transformed into an eigenvalue problem. The matrices in the aforementioned eigenvalue equations are generally of large order. In order to solve these matrix equations with modest and optimal computer memory and storage, we employ the iterative Restarted Arnoldi Algorithm in conjunction with the so-called tensor trick method. Furthermore, we incorporate a polynomial accelerator in the algorithm to obtain rapid convergence. We applied the method to obtain the binding energies of Triton, Carbon-12, and Ozone molecule. / Physics / M.Sc (Physics)

No description available.

Energias de ligação para excitons ligados por impurezas doadoras no ZnSe e CdS são calculadas pelo Método Adiabático Hiperesférico. Os acoplamentos não adiabáticos são incluídos na equação radial levando a valores de energias menores que os valores variacionais encontrados na literatura. Estados ressonantes, similares a estados autoionizantes em átomos de dois elétrons, são obtidos acima do primeiro limiar de ionização elétron-impureza. / Binding energy for excitons trapped by impurities in ZnSe and CdS are calculated withing the hyperspherical adiabatic approach. The non adiabatic couplings are included in the radial equations leading to energies lower than the variational values available in the literature. Resonant states similar to autoionizing lines in atoms are predicted to lie above the first electron-impurity ionization threshold.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / by Sean Kevin Collins. / Ph.D.

<div>After completion of a resupply mission to NASA’s proposed Lunar Orbital Platform - Gateway, safe disposal of the Logistics Module is required. One potential option is disposal to heliocentric space. This investigation includes an exploration of the trajectory escape dynamics from an Earth-Moon L2 Near Rectilinear Halo Orbit (NRHO). The effects of the solar gravitational perturbations are assessed in the Bicircular Restricted 4-Body Problem (BCR4BP), as defined in the Earth-Moon rotating frame and in the Sun-B1 rotating frame, where B1 is the Earth-Moon barycenter. Disposal trajectories candidates are classified in three outcomes: direct escape, in direct escapes and captures.</div><div>Characteristics of each outcome is defined in terms of three parameters: the location of the apoapses within to the Sun-B1 rotating frame, a characteristic Hamiltonian value, and the osculating eccentricity with respect to the Earth-Moon barycenter. Sample trajectories are presented for each outcome. Low-cost disposal options are introduced.</div>

La méthode dite de la fonctionnelle de la densité d'énergie (EDF) est l'outil théorique de référence pour l'étude systématique de la structure des noyaux atomiques de masse A>20. La méthode EDF est formulée en deux étapes successives consistant à briser puis à restaurer les symétries du Hamiltonien nucléaire sous-jacent. La technique de restauration des symétries n'est cependant rigoureusement formulée que si la fonctionnelle d'énergie dérive explicitement d'une interaction effective, i.e. d'un pseudo-potentiel, ce qui constitue un cas particulier de la méthode EDF plus générale. Ainsi, et comme cela a été démontré récemment, l'utilisation des paramétrisations existantes des fonctionnelles d'énergie conduit à l'obtention de résultats non physiques. Le pouvoir prédictif limité des fonctionnelles d'énergie existantes et leur inocuité relative à la restauration des symétries, nécessitent aujourd'hui de repenser leur méthode de construction. La première partie de ce travail a été dédié à l'analyse approfondie du problème associé à la restauration de symétrie et à l'identification de pistes permettant de contraindre la forme analytique des fonctionnelles d'énergie ne dérivant pas d'un pseudo-potentiel indépendant du système. La seconde partie a consisté à développer un pseudo-potentiel rendant la restauration des symétries automatiquement bien définie. Les difficultés de ce travail ont résidé dans (i) l'identification de la complexité minimale du pseudo-potentiel nécessaire à l'obtention d'une fonctionnelle d'énergie assez flexible pour égaler, et si possible améliorer, les performances des paramétrisations existantes, (ii) la dérivation analytique de la fonctionnelle et des champs à un corps découlant de celle ci, (iii) l'implémentation de ces derniers dans les codes de calculs, et dans (iv) le développement d'un protocole d'ajustement des paramètres adapté à la nouvelle fonctionnelle d'énergie ainsi développée. Les premiers résultats obtenus ont permis de valider l'approche en démontrant la flexibilité suffisante du pseudo-potentiel au niveau des calculs réalisés sans restauration des symétries. / The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are (i) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, (ii) the tedious analytical derivation of the functional and of the associated one-body fields, (iii) the implementation of the latter in existing codes, and (iv) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as state-of-the-art (quasi) bilinear functionals.

The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are (i) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, (ii) the tedious analytical derivation of the functional and of the associated one-body fields, (iii) the implementation of the latter in existing codes, and (iv) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as state-of-the-art (quasi) bilinear functionals.

<p>High-precision differential cross section data of the neutron-deuteron elastic scattering reaction at 95 MeV are presented. The neutron-proton scattering differential cross section was also measured and used as a reference to allow an accurate absolute normalization of the neutron-deuteron data.</p><p>Two multi-detector arrays were used, MEDLEY and SCANDAL, at the neutron beam facility at The Svedberg Laboratory in Uppsala. Three different configurations of the detectors allowed to perform three independent measurements. The first experiment involved detecting recoil deuterons from thin deuterated polyethylene targets with the MEDLEY setup and allowed a large angular coverage. In the second experiment, high-precision data were obtained at neutron backward angles, using the SCANDAL setup with the same technique. For the third experiment, data were obtained in the forward angular range using the SCANDAL setup with a technique where neutrons scattered on heavy water were detected by neutron-proton conversion in plastic scintillators and tracking the protons through the detectors. Events from elastic neutron-deuteron scattering were identified in the data analysis, and differential cross sections were obtained after applying corrections and evaluating systematic uncertainties due to effects which could affect the shape or the absolute normalization of the data.</p><p>The results are compared with modern Faddeev calculations using realistic nucleon-nucleon potentials combined with three-nucleon interactions. The effects of three-nucleon forces are expected to increase the differential cross section by about 30% in the region of the minimum. The data agree with this prediction, thus providing evidence for three-nucleon force effects.</p>

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.

High-precision differential cross section data of the neutron-deuteron elastic scattering reaction at 95 MeV are presented. The neutron-proton scattering differential cross section was also measured and used as a reference to allow an accurate absolute normalization of the neutron-deuteron data. Two multi-detector arrays were used, MEDLEY and SCANDAL, at the neutron beam facility at The Svedberg Laboratory in Uppsala. Three different configurations of the detectors allowed to perform three independent measurements. The first experiment involved detecting recoil deuterons from thin deuterated polyethylene targets with the MEDLEY setup and allowed a large angular coverage. In the second experiment, high-precision data were obtained at neutron backward angles, using the SCANDAL setup with the same technique. For the third experiment, data were obtained in the forward angular range using the SCANDAL setup with a technique where neutrons scattered on heavy water were detected by neutron-proton conversion in plastic scintillators and tracking the protons through the detectors. Events from elastic neutron-deuteron scattering were identified in the data analysis, and differential cross sections were obtained after applying corrections and evaluating systematic uncertainties due to effects which could affect the shape or the absolute normalization of the data. The results are compared with modern Faddeev calculations using realistic nucleon-nucleon potentials combined with three-nucleon interactions. The effects of three-nucleon forces are expected to increase the differential cross section by about 30% in the region of the minimum. The data agree with this prediction, thus providing evidence for three-nucleon force effects.