Thesis--University of Wisconsin--Madison. / Typescript. Vita. Includes bibliographical references (leaf 117).

Thesis (Ph.D.)--McMaster University, 2004. / Advisor: Rajat Bhaduri. Includes bibliographical references ( p. 162-168). Also available online.

Few and many-body systems usually feature interesting and novel behaviors compared with their counterparts in three dimensions. On one hand, low dimensional physics presents challenges due to strong interactions and divergences in the perturbation theory; On the other hand, there exist powerful theoretical tools such as the renormalization group and the Bethe ansatz. In this thesis, I discuss two examples: three interacting bosons in two dimensions and interacting bosons/fermions in one dimension. In both examples, there are intraspecies repulsion as well as interspecies attraction, producing a rich spectrum of phenomena. In the former example, a universal curve of three-body binding energies versus scattering lengths is obtained efficiently by evolving a matrix renormalization group equation. In the latter example, exact solutions for the BCS-BEC crossover are obtained and the unexpected robust features in their excitation spectra are explained by a comprehensive semiclassical analysis.

<p>We have performed a measurement of the photodisintegration of the lithium isotopes, 6Li and 7Li, using a monochromatic, polarised photon beam and a segmented neutron detector array which covers approximately 1/4 of 4Î srad. Using time-of-flight and scintillator light-output spectra we separate the data into individual reaction channels. This work is motivated by the need to compare with recent theoretical predictions and to provide data for future theoretical work. <p>For the photodisintegration of 6Li we took data at 12 photon energies between 8 and 35 MeV. We describe the data using a model consisting of two-body reaction channels and obtain angular distributions and absolute cross sections for many of these reaction channels. We compare our results with a recent Lorentz integral transform calculation (Bacca et al. Phys. Rev. C 69, 057001 (2004)). Our results are in reasonable agreement with the calculation, in contradiction with previous experimental results. <p>For the photodisintegration of 7Li, we took data at 9 photon energies between 10 and 35 MeV. We obtain cross sections for the reaction channel 7Li + Á ¨ n + 6Li(g.s.) at all photon energies with angular distributions at all but the highest energy. We obtain angular distributions and total cross sections for reaction channels involving excited states of the daughter nucleus, 6Li, at select energies. We hope that these measurements will provide incentive for new theoretical calculations. <p>We observe neutrons that can only be described by the reaction channel 7Li+Á ¨ n+6Li(10.0) which necessitates an excited state of 6Li with excitation energy Ex = 10.0 } 0.5 MeV that is not in the standard tables of excited states.

<p>We have performed a measurement of the photodisintegration of the lithium isotopes, 6Li and 7Li, using a monochromatic, polarised photon beam and a segmented neutron detector array which covers approximately 1/4 of 4Î srad. Using time-of-flight and scintillator light-output spectra we separate the data into individual reaction channels. This work is motivated by the need to compare with recent theoretical predictions and to provide data for future theoretical work. <p>For the photodisintegration of 6Li we took data at 12 photon energies between 8 and 35 MeV. We describe the data using a model consisting of two-body reaction channels and obtain angular distributions and absolute cross sections for many of these reaction channels. We compare our results with a recent Lorentz integral transform calculation (Bacca et al. Phys. Rev. C 69, 057001 (2004)). Our results are in reasonable agreement with the calculation, in contradiction with previous experimental results. <p>For the photodisintegration of 7Li, we took data at 9 photon energies between 10 and 35 MeV. We obtain cross sections for the reaction channel 7Li + Á ¨ n + 6Li(g.s.) at all photon energies with angular distributions at all but the highest energy. We obtain angular distributions and total cross sections for reaction channels involving excited states of the daughter nucleus, 6Li, at select energies. We hope that these measurements will provide incentive for new theoretical calculations. <p>We observe neutrons that can only be described by the reaction channel 7Li+Á ¨ n+6Li(10.0) which necessitates an excited state of 6Li with excitation energy Ex = 10.0 } 0.5 MeV that is not in the standard tables of excited states.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-30Bitstream added on 2014-06-13T20:27:57Z : No. of bitstreams: 1 ventura_ds_me_ift.pdf: 470589 bytes, checksum: 7a9dc11d67fbc536096e87c18acc1e7c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho investigamos a universalidade em sistemas de três e quatro bósons através do cálculo das suas energias de ligação e dos raios quadráticos médios. Utilizando duas funções de escala calculadas com um potencial de alcance zero e um potencial de alcance finito corrigimos em primeira ordem em r0/a (r0 e a são, respectivamente, o alcance efetivo do potencial e o comprimento de espalhamento de dois corpos) o ponto onde os estados excitados de três corpos desaparecem. Estudamos também as estruturas dos estados de quatro corpos associados ao estado fundamental de três corpos para energia de dois corpos igual a zero. Esses estados são formados predominantemente por uma configuração do tipo 3+1. Os cálculos foram realizados no espaço das configurações usando um método variacional / In this work we investigated the universality in three- and four-boson systems calculating their energies and root-mean-square radii. Using two scaling functions calculated with a zero and a finite range potentials, we corrected to first order in r0/a (r0 and a are, respectively, the effective range of the potential and the two-body scattering length) the point where the three-body excited states disappear. We also studied the structures of the four-body statestied to the three-body ground state for a two-body energy equal zero. These states are predominantly composed by a 3+1 configuration. The calculations were performed in the configuration space using a variational method

Orientador: Marcelo Takeshi Yamashita / Banca: Tobias Frederico / Banca: Renato Higa / Resumo: Neste trabalho investigamos a universalidade em sistemas de três e quatro bósons através do cálculo das suas energias de ligação e dos raios quadráticos médios. Utilizando duas funções de escala calculadas com um potencial de alcance zero e um potencial de alcance finito corrigimos em primeira ordem em r0/a (r0 e a são, respectivamente, o alcance efetivo do potencial e o comprimento de espalhamento de dois corpos) o ponto onde os estados excitados de três corpos desaparecem. Estudamos também as estruturas dos estados de quatro corpos associados ao estado fundamental de três corpos para energia de dois corpos igual a zero. Esses estados são formados predominantemente por uma configuração do tipo 3+1. Os cálculos foram realizados no espaço das configurações usando um método variacional / Abstract: In this work we investigated the universality in three- and four-boson systems calculating their energies and root-mean-square radii. Using two scaling functions calculated with a zero and a finite range potentials, we corrected to first order in r0/a (r0 and a are, respectively, the effective range of the potential and the two-body scattering length) the point where the three-body excited states disappear. We also studied the structures of the four-body statestied to the three-body ground state for a two-body energy equal zero. These states are predominantly composed by a 3+1 configuration. The calculations were performed in the configuration space using a variational method / Mestre

Orientador: Marcelo Takeshi Yamashita / Banca: Lauro Tomio / Banca: Marijana Brtka / Resumo: 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 / Abstract: 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 / Mestre

The analysis of scattering data is usually done by fitting the S-matrix at real experimental energies. An analytic continuation to complex and negative energies must then be performed to locate possible resonances and bound states, which correspond to poles of the S-matrix. Difficulties in the analytic continuation arise since the S-matrix is energy dependent via the momentum, k and the Sommerfeld parameter, η, which makes it multi-valued. In order to circumvent these difficulties, in this work, the S-matrix is written in a semi-analytic form in terms of the Jost matrices, which can be given as a product of known functions dependent on k and η, and unknown functions that are entire and singled-valued in energy. The unknown functions are approximated by truncated Taylor series where the expansion coefficients serve as the data-fitting parameters. The proper analytic structure of the S-matrix is thus maintained. This method is successfully tested with data generated by a model scattering potential. It is then applied to α12C scattering, where resonances of 16O in the quantum states Jρ =0+, 1−, 2+, 3−, and 4+ are located. The parameters of these resonances are accurately determined, as well as the corresponding S-matrix residues and Asymptotic Normalisation Coefficients, relevant to astrophysics. The method is also applied to dα scattering to determine the bound and resonance state parameters, corresponding S-matrix residues and Asymptotic Normalisation Coefficients of 6Li in the 1+, 2+, 3+, 2−, and 3− states. / Thesis (PhD)--University of Pretoria, 2020. / National Research Foundation (NRF) / Physics / PhD / Unrestricted

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