In this dissertation recent advances in modeling various atomic and molecular systems with quantum mechanical calculations employing explicitly correlated Gaussian functions are presented. The author has utilized multiple approaches and considered a number of approximations to develop optimal calculation frameworks. Electronic and muonic molecules and atoms have been considered. A number of unique calculations have been performed and some novel and interesting results, including high accuracy description of the charge asymmetry in the heteronuclear systems and lifetimes of rotationless vibrational levels of diatomic molecules, have been generated.

From the point of view of the electromagnetic interaction, empirical descriptions of the nucleus involve only a few parameters, one of the most important being the nuclear charge radius. This has been well measured for ground state nuclei, but it is difficult to measure for excited states, since they decay too quickly for conventional methods to be used. We study the atomic transitions in muonic ^{90}Zr and find that the nuclear charge radius of the first excited state can be inferred by measuring the gamma emissions from certain transitions. We find that with 1keV photon resolution, we can infer a difference between the charge radius of the nuclear ground state and first excited state as small as 0.13%. We will work in units where h = c = 4\pi\epsilon_0 = 1 so that e^2 = \alpha \approx 1/137 (unless otherwise specified). Mass, momentum, and energy will have units of eV, whereas distances will be given in eV^{-1}. In qualitative discussion, we will sometimes revert to discussing distances in meters due to the familiarity of typical scales (e.g. nuclear radius, Bohr radius). When working with 4-vectors in Minkowski space, we use the metric convention (+,-,-,-). / Graduate

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Ultra-High Energy Cosmic Rays (UHECR) can only be measured by the detection of Extensive Air Showers (EAS) created by the interaction of the cosmic ray particle with an atmospheric nuclei. The inference of some of the properties of UHECR, like their mass composition, is only possible by the comparison of measurements of EAS observables to predictions from Monte Carlo simulations. The most important source of uncertainties on the description of EAS by the simulations is the modeling of hadronic interactions. For many years it has been known that the hadronic interaction models fail on predicting the EAS observables related to their muonic component. The most evident manifestation of that is called muon deficit problem due to the fact that the number of muons in EAS with energies above 1018 eV predicted by simulations is smaller than the observed ones. The aim of this thesis is to approach this problem in three distinct fronts. First, a method is developed to interpret measurements of number of muons in terms of cosmic rays composition in despite of the muon deficit problem. Second, an EAS observable which is sensitive to the muon energy spectrum at ground and, consequently, can be used to constrain hadronic interaction models is proposed and tested. Third and final, the muon production in air showers is studied through measurements of hadron production spectra in pion-carbon interactions. / Raios Cósmicos Ultra Energéticos (Ultra-High Energy Cosmic Rays, UHECR) somente podem ser medidos através da detecção dos Chuveiros Atmosféricos Extensos (Extensive Air Showers, EAS) criados pela interação do raio cósmico primário com núcleos atmoféricos. A inferência de algumas propriedados dos UHECRs, como a composição de massa, é possível somente através da comparação entre medidas de observáveis dos EASs com predições geradas por simulações de Monte Carlo. A fonte de incerteza mais importante na descrição de EAS por simulações é a modelagem das interações hadrônicas. Por muitos anos é sabido que os modelos de interação hadrônica falham na predição de observáveis dos EASs relacionados a sua componente muônica. A manifestação mais evidente disso é chamada problema do déficit de múons devido ao fato que o número de múons em chuveiros com energias acima de 1018 eV predito por simulações é menor que os observados. O objetivo desta tese é abordar este problema através de três frentes. Primeiramente, um método é desenvolvido para interpretar as medidas do número de múons em termos de composição de raios cósmicos considerando o problema do déficit de múons. Segundo, a proposta e o teste de um observável que é sensível ao espectro de energia dos múons na superfície e, consequentemente, pode ser usado para discriminar entre os modelos de interação hadrônica. Por último, a produção de múons em chuveiros é estudada através de medidas do espectro de produção de hádrons em interações do tipo píon-carbono.

Ce travail vise à contribuer à l’amélioration de notre connaissance de l’électrodynamique quantique des états liés, par des mesures de haute précision dans des états exotiques de la matière. Bien que notre connaissance de l’électrodynamique quantique des états liés et du problème relativiste à plusieurs corps aient fait des progrès importants ces dernières années, il reste des questions fondamentales dont la résolution nécessite d’augmenter le nombre et la précision des tests expérimentaux. La première partie de ce travail a été réalisée dans le cadre de l’expérience récente sur les ions muoniques d’hélium (μ4He+ et μ3He+) conduite par la collaboration CREMA. Cette expérience vise à fournir de nouvelles valeurs précises pour les rayons de charge moyens des noyaux des isotopes stables de l’hélium. Ces valeurs sont extraites de la mesure du déplacement de Lamb, c’est-à-dire, de la mesure de la différence d’énergie entre les États 2S − 2P. Une mesure des énergies de transition d’une précision d’au moins 50 ppm, permet de déterminer les rayons de charge des noyaux des isotopes d’hélium avec une incertitude de 0,03%, dix fois plus précise que les résultats précédents obtenus à partir de la diffusion d’électrons. La deuxième partie de ce travail a été de réaliser des mesures de haute précision de transitions de rayons X dans des ions fortement chargés, à l’aide d’un spectromètre à double cristal plan. Ces ions étaient produits dans le plasma d’une source d’ions de type ECRIS (electron-cyclotron resonance ion source). Le spectromètre utilisé est non seulement capable de fournir des mesures de haute précision, mais aussi des mesures sans référence à des énergies de transition théorique ou expérimentales. Quatre énergies de transition de n = 2 → n = 1 ont été mesurées pour des ions d’argon de trois états de charge différents, héliumoïde, lithiumoïde et berylliumoïde, avec une précision meilleure que 3 ppm. La largeur naturelle de chaque raie a également été obtenue expérimentalement. Les résultats trouvés sont en excellent accord avec les calculs théoriques les plus récents. / This work aims to provide insight on Bound-State Quantum-Electrodynamics (BSQED) by experimental fundamentals high-precision tests in exotic states of matter. Although BSQED and the relativistic many-body problem have been undergoing important progress, there are still some issues that require the increase of the number and accuracy of experimental fundamental tests. The first part of this work was done within the framework of the recent experiment in muonic helium ions (μ4He+ and μ3He+) by the CREMA collaboration. This experiment, aims to provide new accurate values for the root-mean-square (rms) charge radii of the helium isotopes nuclei that are extracted from the measurement of the Lamb Shift, i.e., the measurement of the energy difference between the 2S − 2P states. With the goal of measuring the transition energies with an accuracy of at least 50 ppm, the rms charge radii of the helium isotopes will be determined with an uncertainty of 0.03%, a factor of ten more precise than previous results obtained from electron scattering. The second part of this work aims the high-precision measurement of x-ray transitions in Highly-Charged Ions (HCI) using a Double-Crystal Spectrometer (DCS). These ions were produced in the plasma of an Electron-Cyclotron Resonance Ion Source (ECRIS). This kind of spectrometer is able not only to provide high-precision measurements but also reference-free measurements, without reference to any theoretical or experimental energy. Four transitions energies from n = 2 → n = 1 have been measured in an argon plasma in three different charge states, He-, Be- and Li-like, with an accuracy of better than 3 ppm. Besides the energies, the natural width of each transition has also been experimentally obtained. The obtained results are in excellent agreement with the most recent theoretical calculations.

Ultra-High Energy Cosmic Rays (UHECR) can only be measured by the detection of Extensive Air Showers (EAS) created by the interaction of the cosmic ray particle with an atmospheric nuclei. The inference of some of the properties of UHECR, like their mass composition, is only possible by the comparison of measurements of EAS observables to predictions from Monte Carlo simulations. The most important source of uncertainties on the description of EAS by the simulations is the modeling of hadronic interactions. For many years it has been known that the hadronic interaction models fail on predicting the EAS observables related to their muonic component. The most evident manifestation of that is called muon deficit problem due to the fact that the number of muons in EAS with energies above 1018 eV predicted by simulations is smaller than the observed ones. The aim of this thesis is to approach this problem in three distinct fronts. First, a method is developed to interpret measurements of number of muons in terms of cosmic rays composition in despite of the muon deficit problem. Second, an EAS observable which is sensitive to the muon energy spectrum at ground and, consequently, can be used to constrain hadronic interaction models is proposed and tested. Third and final, the muon production in air showers is studied through measurements of hadron production spectra in pion-carbon interactions. / Raios Cósmicos Ultra Energéticos (Ultra-High Energy Cosmic Rays, UHECR) somente podem ser medidos através da detecção dos Chuveiros Atmosféricos Extensos (Extensive Air Showers, EAS) criados pela interação do raio cósmico primário com núcleos atmoféricos. A inferência de algumas propriedados dos UHECRs, como a composição de massa, é possível somente através da comparação entre medidas de observáveis dos EASs com predições geradas por simulações de Monte Carlo. A fonte de incerteza mais importante na descrição de EAS por simulações é a modelagem das interações hadrônicas. Por muitos anos é sabido que os modelos de interação hadrônica falham na predição de observáveis dos EASs relacionados a sua componente muônica. A manifestação mais evidente disso é chamada problema do déficit de múons devido ao fato que o número de múons em chuveiros com energias acima de 1018 eV predito por simulações é menor que os observados. O objetivo desta tese é abordar este problema através de três frentes. Primeiramente, um método é desenvolvido para interpretar as medidas do número de múons em termos de composição de raios cósmicos considerando o problema do déficit de múons. Segundo, a proposta e o teste de um observável que é sensível ao espectro de energia dos múons na superfície e, consequentemente, pode ser usado para discriminar entre os modelos de interação hadrônica. Por último, a produção de múons em chuveiros é estudada através de medidas do espectro de produção de hádrons em interações do tipo píon-carbono.