Thesis (MSc (Physics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The overall goal of this project is to study neutron star properties and locate the transition density from the core to the crust using fifteen parameter sets of the effective Skyrme nucleon-nucleon interaction within a method called the dynamical method. Although another approach used to describe nucleon-nucleon interactions called the modified Gogny interaction is briefly discussed in this work, along with a second method for locating the transition density called the thermodynamical method, results using this interaction and method were not generated, but lays some foundation for a PhD project to be undertaken and potentially showing the relation between the interactions and results. The importance of results depends on how well other theoretical approaches to the problem can reproduce those results and to what accuracy. For models to be valid there also has to be good agreement between the theoretical results and known observables. In this project some properties of neutron stars, such as the equation of state, saturation density, binding energy, symmetry energy, slope and incompressibility parameters of symmetry energy are studied. The transition density is located using the dynamical method. Results of the fifteen Skyrme parameter sets show excellent agreement with the published values of the properties of neutron stars and are consistent with their empirical values inferred from nuclear laboratory data, thus validating the use of the Skyrme interactions for describing nuclear matter. / AFRIKAANSE OPSOMMING: Die hoofdoel van hierdie projek is om neutron ster eienskappe te bestudeer en die oorgangsdigtheid vanaf die kors na die kern te vind deur gebruik te maak van vyftien parameter stelle van die effektiewe Skyrme nukleon-nukleon interaksie binne ‘n metode genaamd die dinamiese metode. Alhoewel ‘n ander benadering vir die beskrywing van nukleon-nukleon interaksies, genaamd die gewysigde Gogny interaksie kortliks in hierdie werk beskryf word, asook ‘n tweede metode, genaamd die termodinamiese metode om die oorgangsdigtheid te bepaal, was resultate vir hierdie interaksie en metode nie gegenereer nie, maar l die fondasie vir verdere werk aan ‘n PhD projek wat die verband tussen die twee interaksies en resultate kan wys. Die belangrikheid van resultate hang af van hoe goed ander teoretiese benaderinge tot die problem daardie resultate kan herproduseer en tot watter akkuraatheid. Vir modelle om geldig te wees moet daar ook goeie ooreenkomste wees tussen teoretiese resultate en bekende waarneembare eienskappe. In hierdie projek word sommige eieskappe van neutron sterre, soos die toestandandsvergelyking, versadigingsdigtheid, bindingsenergie, simmetrie-energie, gradiënt en onsaampersbaarheids parameters van die simmetrie-energie bestudeer. Die oorgangsdigtheid word dan gevind deur gebruik te maak van die dinamiese metode. Resultate van die vyftien Skyrme interaksie parameter stelle wys goeie ooreenstemming met die gepubliseerde waardes van die eienskappe van neutron sterre en is konsistent met hulle empiriese waardes afgelei van kern laboratorium data, wat die geldigheid van Skyrme interaksies vir die beskrywing van kernmaterie bevestig.

PACHECO, Mário Henrique Gomes. Propriedades termodinâmicas do oscilador de Dirac e algumas contribuições da função theta de Jacobi. 2007. 65 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2007. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-05-22T20:39:15Z No. of bitstreams: 1 2007_tese_mhgpacheco.pdf: 348432 bytes, checksum: a820f6b5450ff322d4336320ad27ec1d (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-25T21:18:46Z (GMT) No. of bitstreams: 1 2007_tese_mhgpacheco.pdf: 348432 bytes, checksum: a820f6b5450ff322d4336320ad27ec1d (MD5) / Made available in DSpace on 2015-05-25T21:18:46Z (GMT). No. of bitstreams: 1 2007_tese_mhgpacheco.pdf: 348432 bytes, checksum: a820f6b5450ff322d4336320ad27ec1d (MD5) Previous issue date: 2007 / In this work we analyze the three-dimensional Dirac oscillator in a thermal bath. We found that the heat capacity is two times greather than the heat capacity of the one-dimensional Dirac oscillator in the higher temperatures. We begin with the energy spectrum of the three-dimensional Dirac oscillator, then we find the partition functions and others thermodynamics properties; thus we make one comparasion with the one-dimensional Dirac oscillator and non-relativistic harmonic oscillator. We are interested in study numerically the properties thermodynamics of the square well with infinity potencial. In the latter case we have used a Jacobi theta function. / Nesta tese analisamos o oscilador de Dirac tridimensional em um banho térmico. Encontramos que o calor específico do oscilador de Dirac tridimensional é duas vezes maior que o calor específico do oscilador de Dirac unidimensional quando estamos em um regime de altas temperaturas. Inicialmente utilizamos o espectro de energia do oscilador de Dirac tridimensional para encontramos a função de partição e as demais propriedades. Assim procedendo, fizemos uma comparação com oscilador de Dirac unidimensional e com oscilador harmônico não-relativístico. Em seguida, fizemos um estudo numérico das propriedades termodinâmicas de um poço quadrado de potencial infinito. Para este estudo nós utilizamos a função theta de Jacobi.

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Orientadores: Stefano De Leo, Marcelo Moraes Guzzo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-23T16:45:38Z (GMT). No. of bitstreams: 1 Maia_GabrielGulak_M.pdf: 1857100 bytes, checksum: 8af9898714b92a166704c01eafe1b9fa (MD5) Previous issue date: 2013 / Resumo: A interação de elétrons com barreiras de potencial é um problema bem conhecido da teoria quântica não-relativística de Schrödinger. O tratamento intrinsecamente relativístico do sistema, entretanto, por meio da teoria de Dirac, nos revela diferentes aspectos não fornecidos pela teoria precedente. Por exemplo, uma vez que a equação de Dirac contém naturalmente os graus de liberdade de spin, quatro coeficientes são necessários para descrever o processo e assim o fenômeno da inversão de spin, também chamado spin flip, surge. Com o objetivo de introduzir o formalismo teórico e a notação sobre a qual se sustenta este trabalho, o primeiro capítulo é dedicado a uma breve revisão da equação de Dirac, discutindo-se as propriedades de suas matrizes, a equação de continuidade e obtendo-se suas soluções livres. No capítulo 2 o sistema de interesse, a interação planar de partículas de Dirac com barreiras de potencial eletrostático, é apresentado e são destacados os aspectos que o diferenciam de seu equivalente não-relativístico. São definidos os potenciais escalar e eletrostático e as zonas cinemáticas estabelecidas para os casos unidimensional e bidimensional. O terceiro capítulo é reservado à obtenção dos coeficientes de reflexão e transmissão com e sem spin flip para partículas de Dirac difundindo planarmente através de uma barreira quadrada de potencial eletrostático. Este objetivo é alcançado através de dois métodos distintos de interpretações complementares: O método de degraus e o cálculo de barreira. Coeficientes não-nulos são obtidos para todos os casos, exceto para a transmissão através da barreira com inversão de spin, contrastando com o fato de que todos os degraus componentes da barreira apresentam coeficientes associados diferentes de zero. No quarto capítulo analisa-se o spin das partículas incidentes e o efeito da barreira sobre o spin das partículas refletidas. Ainda que o limite para baixas velocidades seja sempre 1/2, como esperado, em regimes relativísticos encontra-se uma dependência do valor médio deste operador com a energia e o ângulo de incidência no potencial. No quinto capítulo o formalismo de pacote de ondas é desenvolvido e a coerência dos pacotes em relação 'a barreira de potencial investigada, mostrando que a probabilidade de transmissão torna-se constante conforme a largura da barreira aumenta, o que caracteriza o regime incoerente de partículas. Ao fim do capítulo são derivadas as expressões para o spin incidente, refletido e transmitido nesse formalismo. Por fim, o sexto capítulo é reservado ao estudo introdutório do valor médio de autoestados do operador de spin através do formalismo desenvolvido no capítulo anterior como primeira mostra das possibilidades de trabalhos futuros. Mostrado que se o bispinor incidente não for um autoestado do Hamiltoniano de Dirac uma dependência temporal é verificada no valor médio / Abstract: The interaction of electrons with potential barriers is a well-known problem of the Schr¨odinger¿s non-relativistic quantum theory. The intrinsically relativistic treatment of the problem, however, through the Dirac¿s theory, reveals us different aspects, do not provided by the preceding theory. For instance, since the Dirac equation naturally contains the spinorial degree of freedom, four coefficients are needed in order to describe the process and so the spin flip phenomenon emerges. To introduce the theoretical formalism and the notation upon which this work is sustained, the first chapter is devoted to a short review of the Dirac equation, discussing the properties of its matrices, the continuity equation and obtaining its free solutions. Chapter 2 presents the system of interest, the planar interaction of Dirac particles with electrostatic potential barriers. It also highlights the aspects that differentiate this system from its non-relativistic analogue. The scalar and electrostatic potentials are defined and the kinematic zones established for the one-dimensional and the two-dimensional cases. The third chapter is reserved for obtaining the spin flip and spin conserving transmission and reflection coefficients for Dirac particles diffusing two-dimensionally through a square electrostatic potential barrier. This goal is achieved by means of two distinct methods of complementary interpretations: The barrier calculation and the steps calculation. Non-zero coefficients are obtained in all the cases except for the spin flip transmission, contrasting with the fact that no coefficient of the individual steps that compose the barrier is null. In the fourth chapter the incident particles¿ spin is analysed as well as the effect of the barrier on the spin of the reflected particles. As expected the low velocities limits gives us a spin value of 1/2 but in relativistic regime there is a dependence of the spin with the energy and the incidence angle into the potential. In the fifth chapter the wave packet formalism is developed and the packets¿ coherence is investigated, showing that the transmission probability becomes constant as the barrier width becomes greater, characterizing the incoherence of the particle limit. At the end of the chapter the expressions for the incident, reflected and transmitted spin in the new formalism are derived. Finally, the sixth chapter is reserved to the introductory study of mean values of the spin operator eigenstates through the formalism developed in the previous chapter as an example of possibilities for future investigations. It is shown that if the incident bispinor is not a Dirac Hamiltonian eigenstate there is a time dependence in the expected value. Key-words: Relativistic Quantum Mechanics, potential barriers, wave-packets / Mestrado / Física / Mestre em Física

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

Cette thèse porte sur l'étude de modèles non linéaires issus de la mécanique quantique relativiste.Dans la première partie, nous démontrons à l'aide d'une méthode de tir l'existence d'une infinité de solutions d'équations de Dirac non linéaires provenant d'un modèle de hadrons et d'un modèle de la physique des noyaux.Dans la seconde partie, nous prouvons par des méthodes variationnelles l'existence d'un état fondamental et d'états excités pour deux modèles de la physique des hadrons. Par la suite, nous étudions la transition de phase reliant les deux modèles grâce à la Gamma-convergence.La dernière partie est consacrée à l'étude d'un autre modèle de hadrons dans lequel les fonctions d'onde des quarks sont parfaitement localisées. Nous énonçons quelques résultats préliminaires que nous avons obtenus. / This thesis is devoted to the study of nonlinear models from relativistic quantum mechanics.In the first part, we show thanks to a shooting method, the existence of infinitely many solutions of nonlinear Dirac equations of two models from the physics of hadrons and the physics of the nucleus.In the second part, we prove thanks to variational methods the existence of a ground state and excited states for two models of the physics of hadrons. Next, we study the phase transition which links the models thanks to the $\Gamma$-convergence.The last part is devoted to the study of another model from the physics of hadrons in which the wave functions are perfectly confined. We give some preliminary results.