Progress in the description of stellar evolution is driven by the collaborative effort of nuclear physics, astrophysics and astronomy. Using those developments, the theory of the origin of elements in the Universe is challenged. This thesis addresses the problem behind the abundance of 44Ti and the origin of 26Al. The mismatch between the predicted abundance of 44Ti as produced by the only sites known to be able to create 44Ti, core collapse supernovae (CCSNe), and the observations, highlight the current uncertainty that exists in the physics of these stars. Several satellite based γ-ray observations of the isotope 44Ti have been reported in recent times and confirm the disagreement. As the amount of this isotope in stellar ejecta is thought to critically depend on the explosion mechanism, the ability to accurately model the observed abundance would be a pivotal step towards validating that theory. The most influential reaction to the amount of 44Ti in supernovae is 44Ti(α, p)47V. Here we report on a direct study of this reaction conducted at the REX-ISOLDE facility, CERN. The experiment was performed at a centre of mass energy 4.15±0.23 MeV, which is, for the first time, well within the Gamow window for core collapse supernovae. The experiment employed a beam of 44Ti extracted from highly irradiated components of the SINQ spallation neutron source of the Paul Scherrer Institute. No yield above background was observed, enabling an upper limit for the rate of this reaction to be determined. This result is below expectation, suggesting that the 44Ti(α, p)47V reaction proceeds more slowly than previously thought. Implications for astrophysical events, and remnant age, are discussed. In Wolf-Rayet and asymptotic giant branch (AGB) stars, the 26gAl(p,γ)27Si reaction is expected to govern the destruction of the cosmic γ-ray emitting nucleus 26Al. The rate of this reaction, however, is highly uncertain due to the unknown properties of several resonances in the temperature regime of hydrogen burning. We present a high-resolution inverse kinematic study of the 26gAl(d, p)27Al reaction as a method for constraining the strengths of key astrophysical resonances in the 26gAl(p,γ)27Si reaction. In particular, the results indicate that the resonance at Er = 127 keV in 27Si determines the entire 26gAl(p, γ)27Si reaction rate over almost the complete temperature range of Wolf-Rayet stars and AGB stars. The measurements of spectroscopic factors for many states in 27Al and a shell model calculation of nuclear properties of rp-resonant states in 27Si also allow for testing the structure model.

La réponse linéaire de la théorie de la fonctionnelle de la densité dépendante du temps est étudiée dans le cadre du formalisme d'ondelettes du code BigDFT, qui permet d'exprimer les fonctions d'onde électroniques sur une grille de simulation dans l'espace réel. L'objectif est de déterminer un spectre d'excitations de référence pour un système et un potentiel d'échange-corrélation donnés.Il apparaît que seule une partie du spectre, concernant les transitions entre orbitales liées, peut être facilement amenée à convergence par rapport aux paramètres d'entrée de BigDFT, que sont l'extension de la grille de simulation et le nombre d'orbitales du continuum qui sont considérées pour le calcul des spectres. L'énergie de la dernière orbitale inoccupée utilisée dans les calculs se révèle d'ailleurs être un paramètre plus important que ce nombre d'orbitales inoccupées. La justification vient de l'étude de la complétude des bases formées par les orbitales de l'état fondamental du système. Tout ceci permet de porter un regard neuf sur les résultats obtenus avec le formalisme à base gaussienne, tel qu'implémenté dans le code NWChem.En ce qui concerne la convergence du spectre de plus haute énergie, concernant des transitions entre orbitales occupées et orbitales inoccupées du continuum, l'espoir d'une convergence se heurte au problème du tassement du continuum. Il faut alors songer à une manière différente de capter l'information contenue dans ce continuum.Le formalisme des états résonants, dont les fondements ont été posés lors de la première moitié du XXème siècle, est une piste très encourageante pour cela. Une étude préliminaire dans le cas du puits de potentiel carré à une dimension est donc présentée. La première étape a consisté en la détermination de ces états résonants, dont les énergies et fonctions d'onde sont complexes. Une normalisation a notamment pu leur être attribuée. Il est ensuite montré, sous certaines conditions, que la base formée par les états propres de ce potentiel, dont une partie est constituée par les états du continuum, peut être efficacement remplacée par une base discrète et complète faite d'états résonants. Des applications numériques montreront qu'ils peuvent être avantageusement utilisés pour définir la fonction de Green ou encore calculer la propagation temporelle d'un paquet d'onde. / The linear response on the time-dependent density functional theory is studied in the wavelets formalism used in the BigDFT code, that allows the representations of electronic wave-functions on a simulation grid in real space. The goal of this study is to determine a reference excitation spectrum for a given system and exchange-correlation potential.It appears that only one part of the spectrum can be easily brought to convergence with respect to the input parameters of BigDFT, which are the simulation grid extension and the number of unoccupied continuum orbitals considered in the spectrum calculation. The energy of the last unoccupied orbital used actually proves to be more important as a parameter than this number of unoccupied orbitals. This is justified by the study of the completeness of the basis sets made of the ground state orbitals of the system. This gives another point of view regarding spectrum obtained by using the Gausian basis sets formalism, as the one implemented in the code NWChem.As to the convergence of the spectrum at higher energy, concerning transitions between occupied orbitals and unoccupied orbitals of the continuum, the hope for a convergence faces the problem of the continuum collapse. One therefore has to think of another way of retrieving the data contained in this continuum.The resonant states formalism, whose foundations were laid in the first half of the 20th century, is very encouraging in this regard. A preliminary study in the case of the one-dimension square well potential is therefore presented. The first step consisted in the determination of these resonant states, whose energies and wavefunctions are complex valued in general. Their normalization was also clearly defined. It is then shown, under certain conditions, that the basis set formed by the eigenstates of this potential, including the continuum states, can be efficiently replaced by a discrete and complete basis set made of resonant states. Numerical applications also show that these states can also be advantageously used to define the Green's function or even compute the time propagation of a wavepacket.

<p>In this thesis I have theoretically studied electron recombination processes with small molecular ions.</p><p>In these kind of processes resonant states are involved. To calculate the potential energy for these states as a function of internuclear distance, structure calculations and scattering calculations have to be performed.</p><p>So far I have been studying the ion-pair formation with in electron recombination with H₃⁺. The cross section for this process has been calculated using different kind of models, both a time dependent quantum mechanical and a semiclassical.</p><p>I have also studied the direct process of dissociative recombination of HF⁺. To calculate the total cross section for this process, we have performed wave packet propagation on thirty resonant states and summed up the individual cross sections for these states.</p><p>The cross sections for both these processes have a similar appearance to those measured experimentally in the ion storage ring CRYRING in Stockholm.</p>

In this thesis I have theoretically studied electron recombination processes with small molecular ions. In these kind of processes resonant states are involved. To calculate the potential energy for these states as a function of internuclear distance, structure calculations and scattering calculations have to be performed. So far I have been studying the ion-pair formation with in electron recombination with H3+. The cross section for this process has been calculated using different kind of models, both a time dependent quantum mechanical and a semiclassical. I have also studied the direct process of dissociative recombination of HF+. To calculate the total cross section for this process, we have performed wave packet propagation on thirty resonant states and summed up the individual cross sections for these states. The cross sections for both these processes have a similar appearance to those measured experimentally in the ion storage ring CRYRING in Stockholm. / QC 20101103