The nuclear many-body problem is nowadays being increasingly approached on the basis of a relativistic formalism. Microscopic Dirac-Brueckner-Hartree-Fock (DBHF) calculations starting from a realistic nucleon-nucleon interaction seem to be very promising. In the theory of quantum hadrodynamics, nucleons interact through the exchange of virtual mesons and the dynamics is specified by Lorentz covariant Lagrangian densities. In the simplest version, only a vector field (associated with the w meson) accounting for short-range repulsion and a scalar field ("sygma" meson) responsible for attraction are needed to describe saturation in nuclear matter. Calculations in mean field Hartree approximation, neglecting exchange terms and without including any contribution from antiparticles, give an accurate description of many of the features of nuclear systems.The success of semi-classical models in non-relativistic nuclear physics provides a very strong motivation for investigating similar methods in the relativistic context, where only the pure Thomas-Fermi approximation had been studied. In this thesis we set up the semi-classical expansion in relativistic nuclear mean field theory, including gradient corrections of order h(2) to the Thomas-Fermi model, and investigate several applications to nuclear systems.On the basis of Wigner transform techniques, a. recursive scheme to obtain the semi-classical h(2) expansion of the propagator associated with a time-independent single-particle Hamiltonian with matrix structure is presented. We focus our attention on the application of the method to a Dirac Hamiltonian related to relativistic nuclear mean field theory, i.e., including a position-dependent effective mass and the time-like component of a. four-vector field. Compared with the non-relativistic case, the procedure is considerably more complicated owing to the matrix structure of the Hamiltonian. For this reason the "h", expansion is pushed to order h(2) only. A detailed derivation is given of the h(2)-order Wigner-Kirkwood expansion of the relativistic density matrix, in terms of the gradients of the vector and the scalar field, as well as of the expansion of the particle and energy densities. The idempotency of the semi-classical density matrix to second order in "h" is proven. The Wigner-Kirkwood expressions, as they stand, are not suitable to be employed in a self-consistent problem. Therefore, we obtain the corresponding density functional results. In this case the energy densities are expressed as a functional of the local density, the effective mass and their gradients.The accuracy of the Wigner-Kirkwood series is tested on a. relativistic harmonic oscillator and perfect agreement with the Strutinsky averaged observables is found even in the highly relativistic regime. The density functional version is shown to be slightly less accurate, a feature already known in the non-relativistic case. It turns out that the semi-classical expressions represent the different quantities on average, that is, quantum fluctuations are averaged out. This model study shows that, for positive energy states, the derived semi-classical expansions contain all the relativistic ingredients, the difference with quantal results being due mainly to shell effects.Extended Thomas-Fermi calculations, which· include h(2)-order gradient corrections, are performed for relativistic non-linear "sigma"- "omega" models using two kinds of Lagrangians which differ in the form of the scalar coupling for the isoscalar sigma meson. Comparing the semi-classical results of order h(2) (TFh(2)) with the Hartree results, we find that the TFh(2) approximation yields some underbinding when the effective mass (mº) of the model is small, and some overbinding when mº is large. For a value around mº/m = 0.65, both TFh(2) and Hartree would roughly yield the same binding energy. However, since semi-classical and quantal results must differ in the so-called shell energy, this indicates that it is not properly estimated by the TFh(2) approximation.When the h(2)-order gradient corrections are taken into account (TFh(2), we have found a numerical instability in the solution of the semi-classical Klein-Gordon equation obeyed by the scalar field in the case of parameterizations which have mº/m </= 0.60, which can be eliminated if the q-meson mass mº is reduced (with the ratio g(2-0)/m(2-0) unaltered).Second-order corrections in "h" to the TFh(0) approximation improve the agreement with Hartree solutions in a sensitive way, always yielding more bound nuclei than within the Hartree approach. The sign of the h(2) corrections depends on mº, and they are found to vanish around mº/m = 0.75 for the models of the type considered here. In several respects, the semi-classical relativistic phenomenology quite resembles the one met in the non-relativistic regime using Skyrme forces, in spite of the different origin of mº in both situations. Extending the so-called expectation value method to the relativistic problem, and using the TFh(2) semi-classical mean field as a starting point, perturbative quantal solutions are found which are in good agreement with the Hartree results.The semi-classical TFh(0) and TFh(2) density distributions do not present oscillations due to the absence of shell effects, but they average the Hartree results. In the interior of the nucleus the TFh(0) and TF1i2 densities are very similar. However, in the surface and the outer region the TF1i2 densities come appreciably closer than TFh(0) to the Hartree results, due to the gradient corrections incorporated by the TF1i2 functionals, and show an exponential drop off.Liquid drop model coefficients are calculated for some parameter sets of the "sygma-omega" model. We have found reasonable results for the surface thickness and for the surface and curvature energies, which are within the range of the values obtained in non-relativistic calculations using density-dependent Skyrme forces. Therefore, the relativistic effects do not seem to avoid the disagreement of the calculated value of the curvature energy with the empirical value.In this work we also study the effects of the density-dependent Dirac spinor for the nucleons, as is determined microscopically in the DBHF approach, on various properties of the structure and scattering of finite nuclei. To enable this, we construct a relativistic energy density functional that contains the semi-classical kinetic energy density of order h(2). The effective mass and the volume term in the potential energy arise from a DBHF calculation of nuclear matter. This volume term is supplemented by some conventional correction terms and the few free parameters are suitably adjusted. It turns out that the radii of nuclei calculated with the present approach agree better with the experimental value than those obtained in similar studies using a potential energy derived from a non-relativistic G-matrix. This demonstrates that the Dirac effects improve the calculation of ground-state properties of finite nuclei also in our relativistic extended Thomas-Fermi (RETF) approximation.However, this study of ground-state properties is not the main goal of our investigation.The capabilities of our RETF functional are actually appraised in situations in which a full microscopic relativistic calculation, or even a phenomenological one, cannot be easily made, such as nuclear fission of rotating nuclei and heavy ion scattering. In these situations, the method constitutes a reliable tool. For the nuclear fission barriers, the present calculations are the first ones carried out with a relativistic model. We have shown that the model yields results comparable to the non-relativistic ones, with the conceptual-advantage of being relativistic and thus automatically incorporating the spin-orbit force. For the calculations of heavy ion elastic scattering cross sections, we have been able to improve previous results due to achieving a better description of the nuclear, densities.Let us summarize the two apparent merits which the TFh(2) approximation has over the simple TFh(0) one. On the one hand, it provides fully variational densities that go exponential to zero. On the other hand, it takes into account non-local spin-orbit and effective mass contributions up to order h(2), yielding a more reliable average value. / Se establece el desarrollo semi-clásico hasta orden h(2) en la teoría nuclear relativista de campo medio. Así, se obtienen las densidades semi-clásicas relativistas de partículas y de energía para un conjunto de fermiones sometidos a un campo escalar y a un campo vector, en las teorías de campo medio de Wigner-Kirkwood y de Thomas-Fermi, incluyendo correcciones en gradientes hasta orden h(2). El método semi-clásico se aplica a un oscilador armónico relativista. Después se utiliza en modelos T-W no lineales, para los cuales se resuelven las ecuaciones variacionales en núcleos finitos y en materia nuclear semi-infinita. Los resultados semi-clásicos son comparados con los correspondientes resultados cuánticos Hartree.Para estudiar los efectos de los espinores de Dirac para los nucleones sobre diversas propiedades de la estructura y de la dispersión de núcleos finitos, se construye un funcional de la densidad de energía relativista. El funcional contiene la densidad de energía cinética relativista de orden h(2). La masa efectiva y la parte potencial se obtienen a partir de cálculos Dirac-Brueckner de materia nuclear. Se presta especial atención al cálculo de barreras de fisión de núcleos en rotación y del potencial óptico para la dispersión de iones pesados a energías intermedias.

En esta tesis se reformulan de manera detallada la primera aproximación de Born relativista con ondas planas (PWBA), para colisiones inelásticas de electrones, positrones y partículas pesadas con átomos o iones, suponiendo que la función de onda atómica puede describirse mediante un modelo de partículas independientes. Además, se deducen expresiones cerradas de las intensidades de oscilador generalizadas longitudinal (GOS) y transversal (TGOS), y para la intensidad de oscilador óptica (OOS). Un aspecto básico de nuestra formulación es que hemos evitado la aproximación de pequeñas transferencias de momento utilizada por Fano (1963), que altera significativamente las secciones eficaces integradas para energías cercanas al umbral de ionización. Liberada de esta aproximación, la PWBA es idéntica a la DWBA (la aproximación de Born con ondas distorsionadas) en el límite de potencial distorsionador nulo.En la tesis también se describen métodos numéricos robustos para el cálculo de las GOSs longitudinal y transversal, así como esquemas de interpolación y de extrapolación para obtener la la sección eficaz doblemente diferencial (SEDD) a partir de las GOSs tabuladas, que hemos implementado en un conjunto de programas de cálculo. Utilizando el potencial autoconsistente de DHFS, hemos generado una base de datos completa de GOSs, TGOSs, OOSs, y perfiles --Born-Compton' para todas las capas de la configuración del estado fundamental de átomos neutros de los elementos desde el hidrógeno hasta el einstenio. Las GOSs calculadas presentan desviaciones sistemáticas de la regla de suma de Bethe, que son consecuencia de efectos relativistas. A partir de nuestra base de datos de GOSs, hemos calculado secciones eficaces totales, secciones eficaces de frenado, y secciones eficaces de dispersión de energía para colisiones inelásticas de electrones, positrones y protones con átomos libres, integrando numéricamente la SEDD.Teniendo en cuenta las desviaciones de la regla de suma, en esta memoria también se deducen fórmulas asintóticas para las secciones eficaces integradas. Además, a partir de ellas hemos obtenido correcciones de capas directamente, como las diferencias entre estas fórmulas y los valores numéricos de las secciones eficaces. Tanto las desviaciones de la regla de suma como las correcciones de capas se originan principalmente en las capas internas, que son poco sensibles al estado de agregación, por lo que los valores obtenidos son también aproximadamente válidos para colisiones con moléculas y con medios densos.Combinando la PWBA y la DWBA, finalmente en esta tesis se detalla un procedimiento robusto para el cálculo de secciones eficaces de ionización de capas internas por impacto de electrones y positrones, para energías arbitrariamente grandes. Para energías por debajo de 16 veces la energía de ionización, utilizamos la DWBA para determinar las correcciones de distorsión e intercambio a la PWBA. Por encima de esta energía, la PWBA escalada con el factor empírico E/(E+bEa) reproduce fielmente los valores DWBA. Utilizando este esquema, hemos generado una base de datos de secciones eficaces de ionización para las capas K, L y M de todos los elementos desde Z=1 hasta Z=99, por impacto de electrones y positrones con energías entre 50 eV y un 1 GeV. Esta base de datos es útil para el análisis cuantitativo en EPMA y AES, y para la simulación MC del transporte acoplado de electrones y fotones. Hemos implementado esta base de datos en el código PENELOPE, y simulado la generación de rayos x en muestras irradiadas por haces de electrones. La comparación con medidas experimentales confirma que al utilizar DWBA en vez de la PWBA mejora la fiabilidad de las simulaciones. Para facilitar el uso de nuestras secciones eficaces de ionización, hemos parametrizado los valores numéricos mediante expresiones analíticas simples. / We present a detailed formulation of the relativistic plane-wave Born approximation (PWBA) for inelastic collisions of charged particles with free atoms and positive ions. The wave functions of the target atom or ion are calculated from a central-¯eld independent-electron model with the Dirac-Hartree-Fock-Slater self-consistent potential. The double-differential cross section, depending on the energy loss and the recoil energy, is expressed as a sum of two terms which are products of purely kinematical factors and the generalized oscillator strengths (GOSs). Transitions induced by the instantaneous Coulomb interaction between the projectile and the active target electron are described by the longitudinal GOS. Transitions caused by the transverse interaction (exchange of virtual photons) are accounted for by a transverse GOS. We derive closed expressions for the longitudinal and transverse GOSs in terms of vector coupling coefficients and radial integrals. A set of Fortran programs have been written to compute the GOSs, the energy-loss differential cross section and integrals of the latter. We also present systematic derivations of asymptotic formulas for the total cross section, the stopping cross section and the energy-straggling cross section. Shell corrections for these quantities are obtained from the differences between computed numerical values and the predictions of the asymptotic formulas.A method is also described for computing total cross sections for the ionization of inner shells of atoms and positive ions by impact of electrons and positrons with arbitrary energies. The method combines the relativistic PWBA with a semirelativistic version of the distorted-wave Born approximation (DWBA). The difference between the total ionization cross sections that result from the DWBA and the PWBA (considering the longitudinal interaction only) has been calculated numerically for projectiles with kinetic energies up to 16 times the ionization energy of the active shell. In this energy range, ionization cross sections with the accuracy of a distorted-wave calculation are obtained by simply adding this difference to the cross section resulting from the conventional PWBA. For higher energies, the cross section is obtained by multiplying the PWBA cross section by an energy-dependent scaling factor that is determined by a single fitted parameter. Numerical results are shown to agree with experimental data, when these are available.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-05Bitstream added on 2014-06-13T20:08:09Z : No. of bitstreams: 1 castro_lrb_me_guara.pdf: 736041 bytes, checksum: 07f98e709059a4bc8372cdcfd09b4521 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Universidade Estadual Paulista (UNESP) / O estudo dos estados ligados das equações relativísticas têm muitas aplicações em física nuclear e em outras áreas da física, portanto as soluções que apresentam estados ligados usando as equações de Dirac e Klei-Gordon(KG) desempenham um papel importante no interesse dos pesquisadores. A redução a uma dimensão espacial das equações relativisticas permite melhorar o entendimento dos problemas equivalentes em três dimensões de uma maneira fisicamente mais transparente. Esta redução espacial traz como consequência alterações nas estruturas relativísticas dos potenciais que devem ser estudadas. A tarefa de achar estados ligados dessas emoções não é fácil para formas funcionais gerais para os potenciais externos. Neste trabalho as equações de Dirac e KG em um dimensão espacial são investigadas para diferentes tipos de acoplamento e formas funcionais para o potenciais externos que apresentam estados ligados.Um resultado relevantes que para certas misturas convenientes dos potenciais externos as equações de Dirac e KG apresentam as mesmas auto-energias mas diferentes autofunções. O problema em geral pode ser mapeado num problema de Sturm-Liouville encontrando-se soluções de estados ligados exatamente. Discutimos detalhadamente o comportamento das autofunções e auto-energias para partículas e antipartículas obtidas do problema de Sturm-Liouvillee as possíveis soluções isoladas no caso da equação de Dirac. Uma aparente violação do princípio da incerteza em algns casos é remediada com a introdução do conceito de comprimento de onda Compton efetivo, mostrando que a partícula pode ser localizada numa região do espaço arbitrariamente pequena sem a produção de pares partícula-antipartícula. / The study of bound states of the relativistic equations as many applications in nuclear physics and other areas of the physics, therefor the solutions that present bound states for the Dirac and the Klein-Gordon (KG) equations play an important role in the interest of the researches. The reduction to one space dimension of the relativistic equations allows to improve our understanding of the equivalent problems in three dimensionin a physically more transparent way. This space reduction brings as a consequence alterations in the relativistic structures of the potentials that must be studied. The task of findingof these equations is not easy for general functional forms for the external potentials. In this work the Dirac and the KG equationsin one space dimensions for different tpes of coupling and functional forms for the external potentials that present bound states are investigated. A relevant result is that for certain convenient mixtures of the external potentials the Dirac and the KG equations present the same eigenvalues but different eigenfunctins. The problem in general can be mapped into an exactly solvable Sturm-Liouville problem. The behavior of the eigenfunctions and eigenvalues for particles and antiparticles of the Sturn-Liouville problem and the possible isolated solutions in the case of the Dirac equation is discussed in detail. An apparent breaking of the uncertainty priniple in some cases is remedied by the introduction of the concept of effective Compton wavelength, showing that the particle can be located into a region of space arbitrarily small without producing particle-antiparticle pairs.

Nesta dissertação, uma revisão dos modelos cosmológicos newtonianos e neo-newtonianos baseados na formulação da hidrodinâmica clássica é apresentada, com especial ênfase para os resultados básicos e as limitações mais importantes dessas abordagens. Em seguida, mostramos que a descrição Lagrangiana clássica proposta por Lima, Moreira e Santos (1998) para fluidos simples, pode ser generalizada para incluir modelos com misturas de fluidos, e portanto, cosmologias mais realísticas contendo bárions, matéria escura e energia escura, bem como qualquer forma de interação entre essas componentes. Neste trabalho propomos uma descrição lagrangiana clássica para modelos relativísticos do tipo FRW. Nesta descrição, o comportamento dinâmico do fator de escala a(t), como previsto pelas cosmologias relativísticas, é substituído pelo movimento unidimensional de uma partícula teste de massa m sob a ação de um potencial clássico, V(x), onde x é a coordenada unidimensional da partícula. O tratamento pode ser aplicado para os mais diversos cenários de energia escura. Para exemplificar, discutimos com detalhe os seguintes modelos contendo matéria escura e energia escura: XCDM, X(z)CDM, Lambda CDM, Lambda(t) e gás de Chaplygin. Por completeza, modelos multidimensionais do tipo FRW também são considerados. Em todos esses modelos, o parâmetro de curvatura k das seções espaciais das cosmologias determina a energia total da partícula teste pela relação, E=-mk/2, tal como ocorre nos modelos de fluidos simples. As propriedades dinâmicas associadas com o presente estágio de aceleração do universo são univocamente descritas em termos da função potencial do sistema. Finalmente, utilizando os dados da distância de luminosidade provenientes das supernovas do tipo Ia, discutimos como o potencial unidimensional pode ser reconstruído a partir das observações. / In this dissertation, a review of the Newtonian and neo-Newtonian cosmological models based on the classical hydrodynamics formulation is presented with special emphasis to the basic results and the main limitations of such approaches. Next, we show that the classical Lagrangian description as proposed by Lima, Moreira & Santos (1998) for simple fluids, can be generalized to include fluid mixtures, and, therefore, more realistic cosmologies containing baryons, dark matter and dark energy, as well as, any kind of interaction among such components. In the lagrangian description, the dynamic behavior of the scale factor a(t), as predicted by the relativistic cosmologies, is replaced by the unidimensional motion of a test particle with mass m under the action of a classical potential, V(x), where x(t) is the coordinate of the particle. The treatment can be applied for many different scenarios of dark energy. In order to exemplify, we discuss with detail the following models containing dark matter and dark energy: XCDM, X(z)CDM, Lambda(t)CDM and the Chaplygin gas. For completeness, FRW type multidimensional models are also considered. For all these models, the curvature parameter k of the spatial sections in the relativistic cosmologies determines the total energy by the relation, E=-mk/2, as occurs in the simple fluid models. The dynamic property associated with the present accelerating stage of the Universe are univocally described in terms of the potential function of the system. Finally, by using the data from luminosity distance of supernovae type Ia, we discuss how the unidimensional potential can be reconstructed from the observations.

Orientador: Antonio Soares de Castro / Banca: Marcelo Batista Hott / Banca: Alvaro de Souza Dutra / Banca: Bruto Max Pimentel Escobar / Banca: Esdras Santana dos Santos / Resumo: Fazemos uma revisão detalhada de alguns fundamentos básicos do formalismo de Du n- Kemmer-Petiau (DKP). Analisamos as consequências sobre o potencial matricial V para fornecer uma quadricorrente conservada. Também analisamos o comportamento das intera ções vetoriais mínimas e não mínimas sob as transformações de paridade, conjugação de carga e reversão temporal. A ambiguidade do acoplamento eletromagnético (interação vetorial mínima) também é revisada em detalhe. Algums conceitos errados sobre hermiticidade e valores esperados na teoria de DKP difundidos na literatura são discutidos. Além disso, neste trabalho desenvolvemos uma forma alternativa de procurar soluções analíticas da equação de DKP tridimensional (setor spin-0) para o caso de acoplamentos vetoriais (mínimo e não-mínimo). Considerando potenciais com simetria esférica, o problema pode ser mapeado num problema de Sturm-Liouville (da mecânica quântica não relativística) para um dos componentes do espinor de DKP. Neste processo a quadricorrente, a condição de normalização e valores esperados também podem ser expressos em termos desse componente do espinor de DKP de uma forma simples. Como uma aplicação do método desenvolvido, consideramos uma forma linear para os acoplamentos vetoriais. / Abstract: A detailed review of some basics fundamentals of the Du n-Kemmer-Petiau (DKP) formalism is made. The consequences on the potential matrix V for furnish a conserved four-current are analyzed. We also analyze the behavior of minimal and nonminimal vector interactions under parity transformation, charge conjugation and time reversal. The ambiguity of the electromagnetic coupling (minimal vector interaction) is also reviewed in detail. Some misconceptions about the hermiticity and expectation values of the DKP theory widespread in the literature are discussed. In addition, an alternative way to search for analytical solutions of the DKP equation in (3+1) dimensions (spin-0 sector) in the case of vector coupling (minimal and nonminimal) is developed. Considering potentials with spherical symmetry, the problem can be mapped into a Sturm-Liouville problem (nonrelativistic quantum mechanics) for one of the components of the DKP spinor. In this process, the four-current, normalization condition and expectation values can also be expressed in terms of that component of the DKP spinor in a simple way. As an application of the developed method, we consider a linear form for the vector couplings. / Doutor

Made available in DSpace on 2014-06-11T19:32:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-07-05Bitstream added on 2014-06-13T18:43:07Z : No. of bitstreams: 1 castro_lrb_dr_guara.pdf: 373502 bytes, checksum: ce90da31dd1eacd9e0839fbf879727bd (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fazemos uma revisão detalhada de alguns fundamentos básicos do formalismo de Du n- Kemmer-Petiau (DKP). Analisamos as consequências sobre o potencial matricial V para fornecer uma quadricorrente conservada. Também analisamos o comportamento das intera ções vetoriais mínimas e não mínimas sob as transformações de paridade, conjugação de carga e reversão temporal. A ambiguidade do acoplamento eletromagnético (interação vetorial mínima) também é revisada em detalhe. Algums conceitos errados sobre hermiticidade e valores esperados na teoria de DKP difundidos na literatura são discutidos. Além disso, neste trabalho desenvolvemos uma forma alternativa de procurar soluções analíticas da equação de DKP tridimensional (setor spin-0) para o caso de acoplamentos vetoriais (mínimo e não-mínimo). Considerando potenciais com simetria esférica, o problema pode ser mapeado num problema de Sturm-Liouville (da mecânica quântica não relativística) para um dos componentes do espinor de DKP. Neste processo a quadricorrente, a condição de normalização e valores esperados também podem ser expressos em termos desse componente do espinor de DKP de uma forma simples. Como uma aplicação do método desenvolvido, consideramos uma forma linear para os acoplamentos vetoriais. / A detailed review of some basics fundamentals of the Du n-Kemmer-Petiau (DKP) formalism is made. The consequences on the potential matrix V for furnish a conserved four-current are analyzed. We also analyze the behavior of minimal and nonminimal vector interactions under parity transformation, charge conjugation and time reversal. The ambiguity of the electromagnetic coupling (minimal vector interaction) is also reviewed in detail. Some misconceptions about the hermiticity and expectation values of the DKP theory widespread in the literature are discussed. In addition, an alternative way to search for analytical solutions of the DKP equation in (3+1) dimensions (spin-0 sector) in the case of vector coupling (minimal and nonminimal) is developed. Considering potentials with spherical symmetry, the problem can be mapped into a Sturm-Liouville problem (nonrelativistic quantum mechanics) for one of the components of the DKP spinor. In this process, the four-current, normalization condition and expectation values can also be expressed in terms of that component of the DKP spinor in a simple way. As an application of the developed method, we consider a linear form for the vector couplings.