Submitted by JOHN HADDER SANDOVAL QUESADA null (jsandoval@ift.unesp.br) on 2016-03-21T13:14:37Z No. of bitstreams: 1 Thesis.pdf: 687348 bytes, checksum: 6368301fa02619d10860d9db3bec7418 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-03-22T14:28:16Z (GMT) No. of bitstreams: 1 quesada_jhs_me_ift.pdf: 687348 bytes, checksum: 6368301fa02619d10860d9db3bec7418 (MD5) / Made available in DSpace on 2016-03-22T14:28:16Z (GMT). No. of bitstreams: 1 quesada_jhs_me_ift.pdf: 687348 bytes, checksum: 6368301fa02619d10860d9db3bec7418 (MD5) Previous issue date: 2016-01-28 / Outra / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho foca no estudo de sistemas de poucos corpos em duas dimensões no regime universal, onde as propriedades do sistema quântico independem dos detalhes da interação de curto alcance entre as partículas (o comprimento de espalhamento de dois corpos é muito maior que o alcance do potencial). Nós utilizamos a decomposição de Faddeev para escrever as equações para os estados ligados. Através da solução numérica dessas equações nós calculamos as energias de ligação e os raios quadráticos médios de um sistema composto por dois bósons (A) e uma partícula diferente (B). Para uma razão de massas mB/mA = 0.01 o sistema apresenta oito estados ligados de três corpos, os quais desaparecem um por um conforme aumentamos a razão de massas restando somente os estados fundamental e primeiro excitado. Os comportamentos das energias e dos raios para razões de massa pequenas podem ser entendidos através de um potencial do tipo Coulomb a curtas distâncias (onde o estado fundamental está localizado) que aparece quando utilizamos uma aproximação de Born-Oppenheimer. Para grandes razões de massa os dois estados ligados restantes são consistentes com uma estrutura de três corpos mais simétrica. Nós encontramos que no limiar da razão de massas em que os estados desaparecem os raios divergem linearmente com as energias de três corpos escritas em relação ao limiar de dois corpos. / This work is focused in the study of two dimensional few-body physics in the universal regime, where the properties of the quantum system are independent on the details of the short-range interaction between particles (the two-body scatter- ing length is much larger than the range of the potential). We used the Faddeev decomposition to write the bound-state equations and we calculated the three-body binding energies and root-mean-square (rms) radii for a three-body system in two dimensions compounded by two identical bosons (A) and a different particle (B). For mass ratio mB/mA = 0.01 the system displays eight three-body bound states, which disappear one by one as the mass ratio is increased leaving only the ground and the first excited states. Energies and radii of the states for small mass ratios can be understood quantitatively through the Coulomb-like Born-Oppenheimer potential at small distances where the lowest-lying of these states are located. For large mass ratio the radii of the two remaining bound states are consistent with a more sym- metric three-body structure. We found that the radii diverge linearly at the mass ratio threshold where the three-body excited states disappear. The divergences are linear in the inverse energy deviations from the corresponding two-body thresholds. / MEC: 243164-72 / MEC: 243745-72

In this thesis, we study low energy capture reactions and neutron-deuteron elastic scattering using halo effective field theory (EFT). At low energy, EFT provides a general framework to analyze physical systems regarding as an expansion of short-distance over large distance scales. We provide a model-independent calculation for neutron capture on carbon-14, radiative capture of 3He-4He, radiative capture of 3H-4He, and neutrondeuteron (n-d) doublet channel elastic scattering using halo EFT. These reactions play a significant role in the carbon-nitrogen-oxygen (CNO) cycle, solar neutrino flux measurement, lithium production, and big bang nucleosynthesis (BBN) in the early universe. The cross section is calculated for radiative neutron capture in carbon-14 using halo EFT. This reaction is slowest in the CNO cycle, and it acts as a bottleneck in the production of heavier nuclei A greater than 14. The capture contribution is different from Brett-Wigner resonance because of interference between resonant and non-resonant contribution. Also, we calculated, electromagnetic form factors for one-neutron halo nuclei such as carbon-15, beryllium-11, and carbon-19 using EFT. The electromagnetic form factors depend on the nucleon separation energy, effective range, and the two-body current. The EFT expressions are presented to leading order (LO) for 15C and next-to-leading order (NLO) for 11Be and 19C. We also calculated astronomical Sactor for 3He-4He and 3H-4He radiative capture reactions. The low energy Sactor for these reactions are important to understand the Li problem and neutrino physics. At the LO, the capture amplitude contains the initial state swave strong and Coulomb interactions summed to all orders. The NLO contribution comes from non-perturbative Coulomb interaction. Our calculated astrophysical Sactor for 3He- 4He is slightly above the average compared to the other measurement and prediction but consistent within current error bars. The Sactor for 3H-4He is also compatible with the experimental extrapolation. Finally, we studied doublet channel n-d scattering using halo EFT. A two dimer halo EFT is developed to describe the virtual state and three-body bound state in n-d scattering. We show the connection between virtual state and three-body bound state using S-matrix analysis and phase shift analysis which is supported by the Efimov plots.