The first aim of this thesis is to perform relativistic calculation of atomic and ionic polarizabilities and two-photon decay rates. Hydrogenic systems are treated by the Lagrange-mesh method. The extension to alkali-like systems is realized by means of a semiempirical-core-potential approach combined with the Lagrange-mesh method. The studied systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock (DHF) calculation using the GRASP2K package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. Polarizabilities appear in a large number of fields and applications, namely in cold atoms physics, metrology and chemical physics. Two-photon transitions are part of a priori highly unlikely processes and are therefore called forbidden radiative processes. Experimental situations report decays from metastable excited states through these channels. Long lifetimes were measured for highly charged Be-like ions in recent storage-ring experiments, but their interpretation is problematic. The study of the competition between forbidden (one-photon beyond the dipole approximation, or multi-photon) and unexpected (hyperfine-induced or induced by external magnetic fields) radiative processes is all obviously relevant. The second aim of this thesis is to perform relativistic ab initio calculations of electronic isotope-shift (IS) factors by using the multiconfiguration DHF (MCDHF) method implemented in the RIS3/GRASP2K and RATIP program packages. Using the MCDHF method, two different approaches are adopted for the computation of electronic IS factors for a set of transitions between low-lying levels of neutral systems. The first one is based on the estimate of the expectation values of the one- and two-body nuclear recoil Hamiltonian for a given isotope, including relativistic corrections derived by Shabaev, combined with the calculation of the total electron densities at the origin. In the second approach, the relevant electronic factors are extracted from the calculated transition shifts for given triads of isotopes. These electronic quantities together with observed ISs between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Within this computational approach for the estimation of the mass- and field-shift factors, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy, and to estimate theoretical error bars of the IS factors. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Abstract In this thesis, the theory of static magnetic resonance spectral parameters of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy is investigated in terms of the molecular Breit-Pauli Hamiltonian, which is obtained from the relativistic Dirac equation via the Foldy-Wouthuysen transformation. A leading-order perturbational relativistic theory of NMR nuclear shielding and spin-spin coupling tensors, and ESR electronic g-tensor, is presented. In addition, the possibility of external magnetic-field dependency of NMR parameters is discussed. Various first-principles methods of electronic structure theory and the role of one-electron basis sets and their performance in magnetic resonance properties in terms of their completeness profiles are discussed. The presented leading-order perturbational relativistic theories of NMR nuclear shielding tensors and ESR electronic g-tensors, as well as the theory of the magnetic-field dependent NMR shielding and quadrupole coupling are evaluated using first-principles wave function and density-functional theories.

Cette thèse traite de l'application des approches topologiques de la liaison chimique à des systèmes contenant des éléments lourds sujets aux effets relativistes, notamment ceux dépendant du spin. Elle présente deux volets principaux : (i) l'évaluation des effets du couplage spin-orbite (SO) sur la structure électronique à l'aide d'une analyse combinée des propriétés de la fonction ELF et de l'approche QTAIM en deux composantes et (ii) la rationalisation des distorsions structurales pour des molécules impliquant des éléments lourds et le rôle du couplage SO dans ces distorsions. Nous avons pu mettre en évidence différentes situations pour lesquelles le couplage SO peut avoir une influence très importante, modérée ou négligeable. Un résultat important de ce travail démontre la dépendance du couplage SO à son environnement chimique. Pour le second volet, nous avons élaboré une approche qui a consisté à établir une corrélation entre les interactions électrostatiques locales entre régions liantes et non liantes (bassins ELF et QTAIM) et la géométrie moléculaire du système dans l'esprit des modèles VSEPR et du Ligand Close Packing (LCP). Cette approche a notamment mis en évidence la connexion entre la structure moléculaire et les répulsions des paires non-liantes de l'atome central avec leur environnement. / This thesis deals with the aplication of topological approaches of the chemical bonding by means of analysing properties of density-based functions like Electron Localization Function (ELF) and the Quantum Theory of Atoms in Molecumes (QTAIM) to systems involving heavy elements such as 6p elements or actinides . It is divided into two main parts: (i) the evaluation of the spin-orbit coupling (SOC) effects on the electronic structure by means of combination of the QTAIM and ELF topological analyses in the field of quasirelativistic quantum calculations, and (ii) the rationalization of structural distorsions on molecules containing heavy atoms, and the role of the SOC on these distorsions. We were able to emphasize different situations for which SOC has strong, moderate or tiny influence on the chemical bonding, depending on the chemical environnement on which the heavy element is involved. In the second part of this thesis we tested our approach consisting of ELF/QTAIM interbasin repulsion energy analysis in connection with the molecular geometry of the system, in the spirit of the VSEPR and LCP models.

During the past decades, the development of laser technology has produced pulses with increasingly higher peak intensities. These can now be made such that their strength rivals, and even exceeds, the atomic potential at the typical distance of an electron from the nucleus. To understand the induced dynamics, one can not rely on perturbative methods and must instead try to get as close to the full machinery of quantum mechanics as practically possible. With increasing field strength, many exotic interactions such as magnetic, relativistic and higher order electric effects may start to play a significant role. To keep a problem tractable, only those effects that play a non-negligible role should be accounted for. In order to do this, a clear notion of their relative importance as a function of the pulse properties is needed.  In this thesis I study the interaction between atomic hydrogen and super-intense laser pulses, with the specific aim to contribute to the knowledge of the relative importance of different effects. I solve the time-dependent Schrödinger and Dirac equations, and compare the results to reveal relativistic effects. High order electromagnetic multipole effects are accounted for by including spatial variation in the laser pulse. The interaction is first described using minimal coupling. The spatial part of the pulse is accounted for by a series expansion of the vector potential and convergence with respect to the number of expansion terms is carefully checked. A significantly higher demand on the spatial description is found in the relativistic case, and its origin is explained. As a response to this demanding convergence behavior, an alternative interaction form for the relativistic case has been developed and presented. As a guide mark for relativistic effects, I use the classical concept of quiver velocity, vquiv, which is the peak velocity of a free electron in the polarization direction of a monochromatic electromagnetic plane wave that interacts with the electron. Relativistic effects are expected when vquiv reaches a substantial fraction of the speed of light c, and in this thesis I consider cases up to vquiv=0.19c. For the present cases, relativistic effects are found to emerge around vquiv=0.16c .

Les carbures et oxydes des métaux de transition sont d'une importance capitale dans le domaine industriel voir catalytique. Le carbure de tungstène WC a été identifié comme un bon substituant des métaux nobles tel que le platine dans le domaine catalytique. Le but de ce travail de thèse est d'appliquer des méthodes de chimie quantique les plus poussées pour déterminer la structure électronique, la stabilité et la nature de liaison chimique des diatomiques WC et WC2+. Notre recherche préliminaire est motivée par les données spectroscopiques disponibles sur W, W+, W2+, WC et WC2+. La méthodologie adoptée, CASSCF/MRCI/MRCI+Q/aug-cc-pV5Z(-PP) implémentée dans le code MOLPRO, consiste à réaliser des calculs quantique tenant en compte des effets de corrélation et relativistes avec un traitement spécifique du couplage spin−orbite pour la recherche des courbes d'énergie potentielle de l'état fondamental et des états excités de plus basses énergies de WCn+ (n=0-2) tout en utilisant une base suffisamment étendue. Les résultats de ce travail sont en bon accord avec ceux disponibles dans la littérature. En outre, dans ce travail nous avons confirmé pour la première fois que le carbure diatomique dicationique WC2+ est thermodynamiquement stable / Metal carbides and oxides are more interesting in catalytic and industrial domains. Tungsten carbide WC has been detected as serious substituent of platinum Pt catalytic. The ultimate goal of this thesis is theoretical studies of electronic structure, stability and the bound nature on WC, WO and its cations. Our preliminary research were motiving by the available spectroscopic data on W, W+, W2+, WC et WC2+. We used the methodology (CASSCF/MRCI/MRCI+Q/aug-cc-pV5Z(-PP)) implemented on MOLPRO package to perform quantum calculations with high accuracy taking into account the correlation and relativistic effects with a specific treatment of spin orbit coupling for some low lying excited electronic states of WCn+, (n=0, 1 et 2). Our results are shown in good agreement with those available in the literature. Furthermore, in this work for the first time we demonstrated that a carbide dication (WC2+) is thermodynamically stable

Modern solid state chemistry is inconceivable without theoretical treatment of solids thanks to the availability of efficient and accurate computational methods. Being developed mainly by physicist's community and deeply rooted in the formalism of reciprocal space, they often lack connections to familiar chemical concepts, indispensable for the chemical understanding of matter. Quantum chemical topology approach is a powerful theory able to efficiently recover chemical entities from the abstract description of a system given by its density matrices. It can be used to partition any many-electron system into the atoms, using the topology of electron density or for instance into atomic shells, using the topology of ELI-D field. Various characteristics of interactions between these chemical building blocks can be obtained applying bonding indicators, e.g. from the analysis of domain-averaged properties. Quantum chemical topology methods have been extended in the current work for the applications on the diversity of theoretical methods widely used for the description of solids nowadays – from the mean field Kohn-Sham density functional theory to the reduced one-electron density matrices functional theory or from the scalar-relativistic methods to the many-component formalisms employing spinor wavefunctions. It has been shown, that they provide chemically meaningful description of the bonding which is universally applicable to any class of extended systems, be it ionic insulator, covalent solid or metal. It has been shown, that the relativistic effects on the chemical bonding can be easily revealed using extensions of bonding indicators developed in the current work. Classical chemical concepts like Zintl-Klemm concept can be easily recovered with these descriptions. Intimate connection between the class of the material and the degree of chemical bonding delocalization has been also established. All these methods have been successfully applied to the various classes of solids and delivered novel insights on their crystal structure, properties, solid state transitions and reactivity.

This thesis contributes to the field of dark energy and observational cosmology. We have investigated possible direction dependent systematic signal and non-Gaussian features in the supernovae (SNe) Type Ia data. To detect these effects we propose a new method of analysis. Although We have used this technique on SNe Ia data, it is quite general and can be applied to other data sets as well. SNe Ia are the most precise known distance indicators at the cosmological distances. Their constant peak luminosity(after correction) makesthem standard candles and hence one can measure the distances in the universe using SNe Ia. This distance measurement can determine various cosmological parameters such as the Hubble constant, various components of matter density and dark energy from, the SNe Ia observations. Recent SNe Ia observations have shown that the expansion of the universe is currently accelerating. This recent acceleration is explained by invoking a component in the universe having negative pressure and is termed as dark energy. It can be described by a homogeneous and isotropic fluid with the equation of state P = wρ, where w is allowed to be negative. A constant(Λ) in the Einstein equation(known as cosmological constant) can explain the acceleration, in the fluid model it can be modeled with w = -1. Other models of dark energy with w = -1 can also explain the acceleration, however the precise nature of this mysterious component remains unknown. Although there exist a wide range of dark energy models, cosmological constant provides the simplest explanation to the acceleration of the expansion of the Universe. The equation of state parameter w has been investigated by recent surveys but the results are still consistent with a wide range of dark energy models. In order to discriminate among various cosmological models we need an even more precise measurement of distance and error bars in the SNe Ia data. From the central limit theorem we expect Gaussian errors in any experiment that is free from systematic noise. However in astronomy we do not have a control over the observed phenomena and thus can not control the systematic errors (due to some physical processes in the Universe) in the observed data. The only possible way to deal with such data is by using appropriate statistical techniques. Among these systematic features the direction dependent features are more dangerous ones since they may indicate a preferred direction in the Universe. To address the issue of direction dependent features we have developed a new technique(Δ statistic henceforth) which is based on the extreme value theory. We have applied this technique to the available high-z SNe Ia data from Riess et al.(2004)and Riess et al.(2007). In addition we have applied it to the HST data from HST key project for H0 measurement. Below we summarize the material presented in the thesis. Chapter wise summary of the thesis In the first chapter we present an introductory discussion of the various basic cosmological notions eg. Cosmological Principle (CP), observational evidence in support of CP and departures from it, distance measures and large scale structure. The observed departures from the CP could be present due to the systematic errors and/or non-Gaussian error bars in the data. We discuss the errors involved in the measurement process Basics of statistical techniques : In the next two chapters we discuss basics of the statistical techniques used in this thesis and extreme value theory. Extreme value theory describes how to calculate the distribution of extreme events. The simplest of the distributions of the extremes is known as the Gumbel distribution. We discuss features of the Gumbel distribution since it is used extensively in our analysis. Δ statistic and features in the SNe data : In the fourth chapter we derive Δ statistic and apply it to the SNe Ia data sets. An outline of the Δ statistic is as follows : a) We define a plane which cuts the sky into hemispheres. This plane will divide the data into two subsets, one in each hemisphere. b) Now we calculate the χ2 in each hemisphere for an FRW universe assuming a flat geometry. c) The difference of χ2 in the two hemisphere is calculated and maximized by rotating the plane. This maximum should follow the Gumbel distribution. Since it is difficult to calculate the analytic form of Gumbel distribution we calculate it numerically assuming Gaussian error bars. This gives the theoretical distribution for the above calculated maximum of difference of χ2 . The results indicate that GD04 shows systematic effects as well non-Gaussian features while the set GD07 is better in terms of systematic effects and non-Gaussian features. Non-Gaussian features in the H0 data : HST key project measures the value of Hubble constant at the level of 10% accuracy, which requires precise measurement of the distances. It uses various methods to measure distance for instance SNe Ia, Tully-Fisher relation, surface-brightness fluctuations etc. In the fifth chapter we apply Δ statistic to the HST Key Project data in order to check the presence of non-Gaussian and direction dependent features. Our results show that although this data set seems to be free of direction dependent features, it is inconsistent with the Gaussian errors. Analytic Marginalization : The quantities of real interest in cosmology are ΩM and ΩΛ, Hubble constant could in principle be treated as a nuisance parameter. It would be useful to marginalize over the nuisance parameter. Although it can be done numerically using Bayesian method, Δ statistic does not allow it. In chapter six we propose a method to marginalize over H0 analytically. The χ2 in this case is a complicated function of errors in the data. We compare this analytic method with the Bayesian marginalization method and results show that the two methods are quite consistent. We apply the Δ statistic to the SNe data after the analytic marginalization. Results do not change much indicating the insensitivity of the direction de-pendent features to the Hubble constant. A variation to the Δ statistic: As has been discussed earlier that, it is difficult to calculate the theoretical distribution of Δ in general. However if the parent distribution follows certain conditions it is possible to derive the analytic form for the Gumbel distribution for Δ. In the seventh chapter we derive a variation to the Δ statistic in a way that allows us to calculate the analytic distribution. The results in this case are different from those presented earlier, but they confirm the same direction dependence and non-Gaussian features in the data.

Este trabalho descreve o desenvolvimento de um simulador para as câmaras de expansão temporal / detectores de radiação de transição (TEC / TRD) do experimento PHENIX, instalado no Colisor de Íons Pesados Relativisticos (RHIC) do Laboratório Nacional de Brookhaven (BNL) nos EUA. O programa do RHIC prevê a produção e caracterização de um estado da matéria conhecido como plasma de quarks e glúons (QGP), através de colisões entre prótons, dêuterons e íons pesados com energias de centro de massa sqrt(s_NN) entre 20 e 200 GeV. O PHENIX, um dos quatro experimentos instalados no acelerador, é especializado na medida de sinais eletrofracos provenientes das colisões e o TEC / TRD é o único subsistema do PHENIX capaz de identificar elétrons de forma eficiente para momentos acima de 5 GeV/c. Um simulador para reprodução da resposta do detector à passagem de partículas foi desenvolvido e comparado a dados de um detector proporcional monofilar construído no Laboratório de Instrumentação e Partículas da USP, e aos dados do próprio TEC / TRD. Os resultados mostram um acordo razoável entre medidas e simulações. O uso do simulador deverá permitir o estudo de novos métodos e melhoras na capacidade de identificação de elétrons do sistema. / The present work describes the development of a simulator for the Time Expansion Chambers / Transition Radiation Detectors (TEC / TRD) of the PHENIX experiment, installed at the Relativistic Heavy Ion Collider (RHIC) of Brookhaven National Laboratory (BNL). The main goal of the RHIC project is the production and study of a state of matter known as Quark Gluon Plasma (QGP), through collisions of protons, deuterons and heavy ions at center of mass energies sqrt(s_NN) ranging between 20 and 200 GeV. PHENIX, one of the four experiments of the accelerator, is dedicated to measuring electroweak signals arising from the collisions, and TEC / TRD is the only subsystem capable of identifying efficiently electrons with momenta above 5 GeV/c. A simulator to reproduce the detector response to the passage of particles was developed and compared to data from a single wire proporcional counter and from TEC / TRD itself. The results show reasonable agreement between measurements and simulations. The use of the simulator allows studies of new methods and possibly improvements in the electron identification capability of the system.

Relação de dispersão é outro nome para a função Hamiltoniana, cujo conhecimento especica completamente a dinâmica de um sistema no formalismo da mecânica classica. Sua escolha está intimamente vinculada às simetrias do sistema e, no contexto cosmologico aqui apresentado, com as simetrias locais obedecidas pelas leis fsicas. Mais ainda, a contribuição da materia na dinâmica cosmologica reflete a escolha do grupo local de simetrias das leis fsicas. Por outro lado, o problema fundamental da cosmologia pode ser definido como a construção de um modelo de evolução temporal de estados que, sob as hipoteses mais simples sobre estados iniciais (digamos, que demande a menor quantidade de informação possível para serem enunciadas), prediga o estado atual observado. O paradigma inacionario é atualmente a ideia que melhor cumpre esta denição, uma vez que prediz que uma grande variedade de condições iniciais leva a aspectos fundamentais do universo observado. Contudo, os mecanismos usuais de realização da inflação sofrem de problemas conceituais. O ponto de vista deste trabalho e que a realização convencional da inflação, isto é, atraves dos campos escalares minimamente acoplados, é a formulação localmente relativisticamente invariante da inflação. A maneira de incluir quebras e deformações da estrutura de simetrias locais na cosmologia é não única e está associado ao chamado problema trans Planckiano da inflação. Analogamente, a motivação conceitual para incluir esse tipo de modicação tampouco é unica. Dependendo do esquema de realização, a versão localmente não relativstica da mesma pode apresentar graves diculdades de conciliação com observações atuais, ou apresentar vantagens conceituais em relacão ao modelo padrão de inflacão, enquanto em conformidade com observações cosmológicas. Da maneira como foi posto o problema fundamental da cosmologia, a escolha das simetrias locais influi na regra de evolução dos estados. O conceito de simetrias encontra sua formulação independente de teorias físicas no formalismo da teoria de grupos, mas consideraremos uma extensão da ideia, de aplicabilidade mais geral, a teoria das algebras de Hopf que, de certo modo, trata das simetrias de estruturas algebricas. Esta extensão é útil inclusive no trato de simetrias dos espacos não comutativos, uma das principais propostas fsicas que em última analise afeta a estrutura de simetrias locais do espaco-tempo. A expressão simetrias locais, por si só, não diz muito sem a consideração de regras de realização. Essas regras dependem da estrutura matematica das observaveis da teoria. Sob hipoteses muito gerais, que não especicam uma teoria em particular, é possível mostrar, não como um teorema matematico formal, mas como uma hipotese tecnicamente bem motivada, que existem apenas dois tipos de teorias fsicas: as classicas e as quânticas. Trabalharemos sob essas hipoteses, as quais se formulam algebricamente assumindo a estrutura de C*-álgebra para as observaveis físicas, outra motivação para o uso das álgebras de Hopf para descrição das simetrias da natureza. / Dispersion relation is another name for the Hamiltonian function whose knowledge completely specifies the dynamics in the formalism of classical mechanics. Its choice is intimately related to the symmetries of the system, and, in the cosmological context here exposed, with the local space-time symmetries obeyed by physical laws. For the other side, the fundamental problem of cosmology can be defined as a construction of a time evolution model of states which, under simplest possible hypothesis concerning initial conditions (say, which demands the minimal amount of information to be specified), predicts the present observed state. The inflationary paradigm is currently the idea which better accomplishes this definition, since it predicts that a great variety of initial conditions lead to essential aspects of observed universe. The usual mechanisms of inflation suffer, however, with conceptual problems. The point of view of this work is that the usual realization of inflation based on weakly coupled scalar fields is the local relativistic invariant realization. The way of including breaks and deformations of the local space-time symmetries is not unique and it is associated to the so called Trans-Planckian problem of inflation. Analogously, the motivation to include this kind of modification is neither unique. Depending of the scheme of realization, the locally non-relativistic version may lead to serious difficulties in conciliation with observations, or to conceptual advantages over standard formulations while in accordance with observational data. In the way that was proposed the fundamental problem of cosmology, the choice of local symmetries affects the rule of evolution of states. The concept of symmetry finds its formulation independently of physical theories in the group theory formalism, but we will consider an extension of the idea, with wider applicability, the theory of Hopf algebras, which is about symmetries of algebraic structures. That extension is also useful to deal with symmetries of non-commutative spaces, one of the main physical proposals that affects the structure of space-time symmetries. The expression, local symmetries, by itself, does not say too much without considering realization rules. Those rules depend on mathematical structure of observables in the theory. Under very general hypothesis that do not specify a particular theory, it is possible to show, not as a formal mathematical theorem, but as a technically well motivated hypothesis, that only two types of physical theories do exist: The classical ones and the quantum ones. We are going to work under those hypothesis, which can be algebraically formulated assuming a C*-algebra structure for physical observables, another motivation for the use of algebraic structures like Hopf algebras for the description of nature\'s symmetries

Le noyau est par essence un système complexe, composé de fermions composites fortement corrélés, soumis à la fois aux interactions forte, faible et électromagnétique. La description de sa structure interne est un enjeu important de la physique moderne. Ainsi la manière qu'ont les nucléons de s'organiser au sein des noyaux atomiques est le reflet des corrélations auxquelles ils sont soumis. On comprend alors que la complexité des interactions inter-nucléoniques se traduit par une grande richesse de schémas selon lesquels les nucléons se distribuent dans les systèmes nucléaires. Le noyau révèle une structure délocalisée où les nucléons se répartissent de façon quasi-homogène dans le volume nucléaire. Mais il peut également présenter des sous-structures localisées, appelées clusters ou agrégats nucléaires. Ces travaux s’inscrivent dans le cadre des approches de type champ-moyen relativiste (RMF), permettant un traitement universel de la phénoménologie nucléaire. Dans un premier temps, nous exposerons les éléments de formalisme permettant la construction d’une telle approche en partant des interactions fondamentales qui sous-tendent la dynamique nucléonique au sein des noyaux. Néanmoins ce formalisme ne permet pas de rendre compte des propriétés expérimentales des observables nucléaires : une stricte approche de type champ-moyen, néglige de trop nombreuses classes de corrélations. Nous discuterons alors des méthodes existantes pour prendre en compte ces corrélations, de type particule-trou (déformation) ainsi que de type particules-particules (appariement). Dans un premier temps, une nouvelle méthode diagrammatique, permettant une approche perturbative des corrélations est proposée ainsi qu’une implémentation automatisée associée basée sur une théorie combinatoire. Ensuite, nous reviendrons à un traitement phénoménologique des corrélations particules-trous, pour nous focaliser sur l’impact des corrélations particules-particules. En premier lieu nous discuterons le phénomène de formation de paires nucléoniques en utilisant le langage de la théorie des graphes, langage permettant plusieurs simplifications formelles ainsi qu’une compréhension différentes de l’appariement. Les corrélations d’appariement seront tout d’abord prise en compte par une approche de type Hartree-Bogolioubov relativiste. Toutefois ce formalisme ne conservant pas le nombre de particules, nous présenterons une approche projective permettant de le restaurer. L’effet de cette restauration sur le système sera également étudié. Seront ensuite présentés les différentes implémentations et optimisations numériques, développées pendant cette thèse, pour un traitement général des déformations nucléaires. Munis de ces outils, nous reviendrons sur la formation d’agrégats nucléaires, les clusters, comme phénomène émergent issu de la prise en compte de certaines classes de corrélations. Tout d’abord des mesures de localisations et paramètres quantifiant la dispersion des fonctions d’ondes nucléoniques sont proposées, permettant d’analyser le noyau pour localiser et comprendre l’origine de l’agrégation. L’analyse de ces quantités est présentée et permet la première description unifiée de la formation de clusters aussi bien dans les noyaux légers (Néon, Magnésium) que dans les noyaux lourds émetteurs alpha (Polonium). L’émergence des clusters est ensuite décrite au travers du prisme des transitions de phases quantiques. Un paramètre d’ordre est exhibé ainsi que la caractérisation de ce phénomène en tant que transition de Mott. L’influence des corrélations d’appariement sur la formation de clusters est analysée et une étude précise des propriétés spatiales des paires de nucléons est menée pour plusieurs noyaux dans différentes régions de masses. Enfin une méthode de prise en compte de corrélations à 4-corps, dite de quartet est proposée pour tenter d’expliquer l’émergence des clusters en tant que préformation de particules alpha. / The atomic nucleus is intrinsically a complex system, composed of strongly correlated non-elementary fermions, sensitive to strong and electroweak interaction. The description of its internal structure is a major challenge of modern physics. In fact the complexity of the nucleon-nucleon interaction generates correlations which are responsible of the diversity of shapes that the nuclei can adopt. Indeed the nuclei can adopt either quasi-homogeneous shapes when nucleons are delocalized or shapes where spatially localized structure can emerge, namely nuclear clusters. This work is an extension of relativistic mean-fields approach (RMF), which allows an universal treatment of nuclear phenomenology. In a first time we will present the necessary formalism to construct such an approach starting with the fundamental interactions underlying nucleons dynamics within the nucleus. However this approach doesn't allow an accurate reproduction of experimental properties: a purely mean-field approach neglects to many correlations. Existing methods to treat both particle-hole (deformation), particle-particle (pairing) correlations will be discussed. First we will propose a new diagrammatic method, which take correlation into account in a perturbative way, the implementation of this approach using combinatory theory will be discussed. Then we will get back to a phenomenological treatment of particle-hole correlations, to focus on the impact of particle-particle. Formation of nucleonic pair will be discussed in the language of graph theory, allowing several formal simplifications and shed a different light on pairing. Pairing correlations will be at first treated using a relativistic Hartree-Bogolioubov approach. Nevertheless this formalism doesn't conserve particle number, and thus we will present a projective approach to restore it. The effect of this restoration will also be studied. Then to describe general nuclear deformation, several implementations and optimizations developed during this PhD will be presented. With this tools, clusterisation will be investigated as phenomenon emerging for certain class of correlations. Localization measure will be derived allowing a clearer understanding of cluster physics. The analysis of theses quantities makes possible a first unified description of cluster formation both for light nuclei (Neon) or for heavy alpha emitters (Polonium). Cluster emergence will be described as a quantum phase transition, an order parameter will be displayed and this formation will be characterized as a Mott transition. The influence of pairing correlations on cluster formation is studied and a detailed study of pairs spatial properties is performed for nuclei from several mass regions. Lastly a method allowing treatment of 4-body correlations (quartteting) is proposed to explain cluster emergence as alpha particle preformation.