京都大学 / 新制・課程博士 / 博士(理学) / 甲第23701号 / 理博第4791号 / 新制||理||1686(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 永江 知文, 准教授 成木 恵, 教授 中家 剛 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Physics / M. Sc. (Physics)

A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods. / Physics

Physics / M. Sc. (Physics)

A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods. / Physics / M.Sc. (Physics)

Thesis (Ph. D.)--Missouri University of Science and Technology, 2010. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed April 21, 2010) Includes bibliographical references (p. 82-87).

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

<p>  The adiabatic hyperspherical representation has been applied to study few-body systems in both ultracold atomic physics and low energy nuclear physics, as it is a powerful tool that can be used to solve a variety of few-body Hamiltonian's across a wide range of disciplines in physics. In conjunction with the adiabatic hyperspherical representation, we utilized an explicitly correlated Gaussian basis expansion, different from the traditional hyperspherical harmonic expansion typically used with this method. In atomic physics, we applied this method to study the four-body (e^-e^-e⁺e⁺) coulombic system to study positronium-positronium collisions and to get a theoretical value of the 1<em>s</em>-2<em>s</em> scattering length. This work is published in [Phys. Rev. A 100, 012711 (2019)]. We also looked at few-body physics near the unitary limit, particularly near the <em>s</em>- and <em>p</em>-wave unitary limits where the dominant length scale is the scattering length and scattering volume. On this front, we studied universal physics in this regime for the equal-mass system. This work is published in [Phys. Rev. A 106, 023304 (2022)]. This method was further applied to few-body nuclear physics.</p> <p><br></p> <p>  We treat the three and four neutron scattering problems in the <em>N</em>-body continuum to understand and gain insight into possible few-neutron resonances, most notably whether a four-neutron resonance exists. There have been many conflicting theoretical results on whether a four-neutron resonance exists that stemmed from a recent experiment by Kisimori et al. in 2016 [Phys. Rev. Lett. 116, 052501 (2016)]. To provide further theoretical insight on this problem, we use the adiabatic hyperspherical toolkit to probe the scattering continuum and from the 4<em>n</em> density of states, conclude that there is no 4<em>n</em> resonance state. Our work on this is published in [Phys. Rev. Lett. 125, 052501 (2020)] and [Phys. Rev. C 103, 024004 (2021)]. There are other few-body systems in nuclear physics that are explored in the adiabatic hyperspherical representation, including systems like the triton, helium-3, and helium-4 nuclei to visualize and characterize the different reaction pathways the <em>N</em>-body system can fragment into at a given collision energy.</p>

We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.

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