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A recent study of the positronium atom showed that the energy levels could be determined numerically using an effective field theory just as easily as the underlying true theory. Here, we expand on this idea by modeling the three-body positronium-ion and four-body di-positronium molecule with low-energy effective field theories. We then compare the results obtained using the effective theories to those found in a similar manner with the true theory to determine if numerical calculations will converge more quickly using the effective field theory due to removal of the Coulomb divergence. Finally, with the necessary framework in place, we calculate a matrix element needed to evaluate the correction to the magnetic moment of the positronium-ion due to the interaction between the positron and the two electrons which form a spin singlet.

This dissertation work is a study of positronium formation for positron-hydrogen and positron-helium collisions in the Ore gap (the energy region between the threshold for ground-state positronium formation and the first excitation level of the target atom) using variational K-matrices. We have fitted the K-matrices using multichannel effective range theories and using polynomials. Using the variational K-matrices and their fits, we have located zeros in the positronium-formation scattering amplitude and corresponding deep minima in the positronium-formation differential cross section. The zeros are related to the vortices in the extended velocity field associated with the positronium-formation scattering amplitude. For positron-hydrogen collisions, we have found two zeros in the positronium-formation scattering amplitude, and corresponding deep minima in the positronium-formation differential cross section, while we have obtained a zero in the positronium-formation scattering amplitude for positron-helium collisions. We have connected the zeros in the positronium-formation scattering amplitude to vortices in the extended velocity fields. Our work shows that vortices can occur for charge exchange in atomic collisions.

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L’expérience GBAR propose de mesurer, au CERN, l’accélération de la pesanteur terrestre sur l’antimatière grâce à des atomes froids (neV) d’antihydrogène soumis à une chute libre. Ceux-ci sont obtenus en refroidissant d’abord des ions positifs d’antihydrogène, obtenus grâce à deux réactions consécutives se produisant lors de la collision d’un faisceau d’antiprotons avec un nuage dense de positronium.Le travail de thèse porte sur l'étude de ces réactions dans le but d’optimiser la production des ions d’antihydrogène. Pour cela, les sections efficaces des deux réactions ont été calculées dans le cadre d’un modèle de théorie des perturbations (Continuum Distorted Wave – Final State) pour des antiprotons ayant une énergie comprise entre 0 et 30 keV ; différents états excités du positronium ont été examinés. Ces sections efficaces ont ensuite été intégrées à une simulation de la zone d’interaction entre positronium et antiprotons afin de définir les paramètres expérimentaux optimaux pour GBAR. Les résultats suggèrent d’utiliser les états 2P, 3D ou, dans une moindre mesure, 1S du positronium, respectivement pour des antiprotons de 2, moins de 1 ou 6 keV. L’importance de compresser les impulsions temporelles d’antiprotons est soulignée ; le positronium devra être confiné dans un tube de 20 mm de long pour 1 mm de diamètre.Un laser en impulsion à 410 nm permettant d’exciter la transition à deux photons vers l’état 3D du positronium avait déjà été proposé. Son principe repose sur le doublage en fréquence d’un laser titane-saphir à 820 nm. Le dernier volet de la thèse fut dédié à la réalisation de ce laser, qui délivre des impulsions courtes (9 ns) de 4 mJ à 820 nm. / The future CERN experiment called GBAR intends to measure the gravitational acceleration of antimatter on Earth using cold (neV) antihydrogen atoms undergoing a free fall. The experiment scheme first needs to cool antihydrogen positive ions, obtained thanks to two consecutive reactions occurring when an antiproton beam collides with a dense positronium cloud.The present thesis studies these two reactions in order to optimise the production of the anti-ions. The total cross sections of both reactions have been computed in the framework of a perturbation theory model (Continuum Distorted Wave – Final State), in the range 0 to 30 keV antiproton kinetic energy; several excited states of positronium have been investigated. These cross sections have then been integrated to a simulation of the interaction zone where antiprotons collide with positronium; the aim is to find the optimal experimental parameters for GBAR. The results suggest that the 2P, 3D or, to a lower extend, 1S states of positronium should be used, respectively with 2, less than 1 or 6 keV antiprotons. The importance of using short pulses of antiprotons has been underlined; the positronium will have to be confined in a tube of 20 mm length and 1 mm diameter.In the prospect of exciting the 1S-3D two-photon transition in positronium at 410 nm, a pulsed laser system had already been designed. It consists in the frequency doubling of an 820 nm pulsed titanium-sapphire laser. The last part of the thesis has been dedicated to the realisation of this laser system, which delivers short pulses (9 ns) of 4 mJ energy at 820 nm.

L’expérience GBAR repose sur la production d’ions antihydrogène positifs dans le but de mesurer l’accélération gravitationnelle à laquelle est soumise l’antimatière au repos. Le projet ANTION, sous-projet de GBAR, a pour but la production de ces ions d’antimatière. Il vise également à mesurer la section efficace de production d’antihydrogène dans les collisions d’antiprotons sur des atomes de positronium, ainsi que les sections efficaces correspondantes avec la matière, de production d’hydrogène et de l’ion hydrogène négatif. Ces expériences reposent sur la formation d’un nuage très dense de positronium, et nécessitent donc une grande quantité de positons qui seront implantés sur un matériau convertisseur de positons en positronium. Cette thèse décrit la construction d’un piège à “buffer gas” à trois étages, destiné à piéger et accumuler des positons pour le projet ANTION. L’association d’un piège de Penning avec une source basée sur un Linac constitue un montage expérimental unique. Le piège a été construit et optimisé, et est maintenant pleinement opérationnel. Les protocoles de piégeage ont été étudiés et les effets du gaz tampon et du gaz de refroidissement sur le taux de piégeage et la durée de vie des positons ont été quantifiés. Afin de faciliter la mesure de la section efficace de production de l’hydrogène, une simulation avec GEANT4 a été mise au point. Elle décrit l’évolution temporelle et spatiale des atomes d’ortho-positronium dans la cavité où aura lieu la production d’hydrogène. On estime que 2.7 atomes d’hydrogène sont produits pour des proton de 6 keV d’énergie incidente, en utilisant les sections efficaces calculées avec le modèle “Coulomb-Born Approximation”, et 1.6 atomes d’hydrogène pour des protons de 10 keV, si l’on utilise la méthode “two-center convergent close-coupling”. Les simulations permettent également d’estimer le bruit de fond associé aux positons et à l’annihilation du para-positronium. Cette étude amène à proposer une modification permettant d’augmenter le nombre d’atomes de positronium dans la cavité. En parallèle, une étude a porté sur l’efficacité de modération de positons d’une couche épitaxiale de carbure de silicium 4H-SiC. Une efficacité de modération de 65% a été mesurée pour des positons implantés avec une énergie de l’ordre du kilo- électronvolt. Ce résultat intéresse les expériences de physique utilisant des positons lents, car il permet d’améliorer la luminosité de faisceaux de positons; dans le cas de GBAR cela permettrait d’augmenter l’efficacité de piégeage des positons. / The GBAR experiment relies on the production of antihydrogen positive ions to achieve its goal of measuring the gravitational acceleration of antimatter at rest. The ANTION project, included in the GBAR enterprise, is responsible for the production of these antimatter ions. Moreover, it also aims to measure the cross section of antihydrogen production throughout the collision of antiprotons and positronium atoms, as well as the matter cross sections of hydrogen and the hydrogen negative ion. These experiments imply the formation of a very dense positronium cloud, thus a large amount of positrons will be implanted on a positron/positronium converter material. This thesis reports the construction of a three stage buffer gas trap with the goal of trapping and accumulating positrons for the ANTION project. The combination of the Penning-type trap with a LINAC source constitutes a unique experimental setup. The trap was commissioned and optimized and is now fully operational. Trapping protocols were studied and the effect of the buffer and cooling gases on the positron trapping rate and lifetime was assessed. In order to assist the cross section measurement of hydrogen, a GEANT4 simulation was developed. It evaluates the time and spatial evolution of the ortho-positronium atoms in a cavity, where hydrogen production will take place. It was estimated that 2.7 hydrogen atoms are produced for proton impact energy of ∼ 6 keV, according to the cross sections computed with the Coulomb-Born Approximation model, and 1.6 hydrogen atoms for a proton impact energy of ∼ 10 keV, according to the two-center convergent close-coupling method. The simulations also allow the estimation of the background associated with the positron and para-positronium decay. In addition, a suggestion is proposed to increase the number of positronium atoms in the cavity. In parallel, the positron moderation efficiency of a commercially available 4H-SiC epitaxial layer was studied. A 65% moderation efficiency was observed for kiloelectronvolt implanted positrons. This result can be of interest to slow positron physics experiments by improving the brightness of positron beams, and in particular to GBAR as it can potentially increase the efficiency of positron trapping.

Made available in DSpace on 2015-04-22T22:07:21Z (GMT). No. of bitstreams: 1 carlos velas.pdf: 1180958 bytes, checksum: 61ddfdc0eddd3a6683e3d7b9d8715e0b (MD5) Previous issue date: 2013-04-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this dissertation we present a detailed and analytical study of the information entropy using two formalisms. These formalisms are: Shannon entropy and Tsallis entropy. Shannon entropy obeys the principle of additivity, however the Tsallis entropy is nonadditive. These entropies are applied to atomic models of Mochinsky and positronium, which are two-body systems. To determine the entropy, we utilize the wave functions and probability densities for both the atomic models. The Shannon entropy has a logarithmic dependence, while the Tsallis entropy has a dependency on the entropic factor q , known as the Tsallis entropic factor. In our work, entropies were calculated in the position space and also in the momentum space and also using the concept of the principle of Heisenberg inequality adapted for the information entropy. For the Shannon entropy, we have the Bialynici, Birula, and Mycielski uncertainty principle, and Tsallis entropy we use pseudo-uncertainty. Finally we demonstrate graphically the behavior of the entropies of both the formalisms. / Nesta dissertação apresentamos um estudo detalhado e analítico da entropia da informação usando dois formalismos. Estes formalismos são: entropia de Shannon e a entropia de Tsallis, a entropia de Shannon obedece o principio da aditividade, já a entropia de Tsallis é conhecida como entropia não-aditiva. Essas entropias serão aplicadas nos modelos atômicos de Mochinsky e Positrônio, que são sistemas de dois corpos. Para determinar a densidade das entropias, nos utilizamos a função de onda e a densidade de probabilidade para ambos os modelos atômicos. A entropia de Shannon tem uma dependência logarítmica, enquanto a entropia de Tsallis tem uma dependência do fator entrópico q , conhecido como fator entrópico de Tsallis. Em nosso trabalho, as entropias foram calculadas nos espaços das posições e também no espaço dos momentos, com isso utilizamos o conceito do principio da desigualdade de Heisenberg, adaptando para a entropia da informação. Para a entropia de Shannon, temos o principio de incerteza de Bialynici, Birula, and Mycielski, para a entropia de Tsallis chamamos de pseudo-incerteza. Por fim demonstramos graficamente o comportamento das entropias de ambos os formalismos.

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Thesis (Ph.D.)--Memorial University of Newfoundland, 1997. / Bibliography: leaves 102-109.