Triatomic molecules in two-dimensional layers

• Ano de defesa: 2012
• Autor(a) principal: Filipe Furlan Bellotti
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Instituto Tecnológico de Aeronáutica
• Palavras-chave em Português: Problema de poucos corpos; Problema de três corpos; Moléculas triatômicas; Gases; Baixa temperatura; Energia; Física molecular; Física nuclear
• Link de acesso: http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2056

We found universal laws for the spectrum of two-dimensional three-body systems, composed by two identical particles and a distinct one (AAB). These universal laws appear when the potential range (r_0) is much smaller than the size of the system. In two dimensions this condition is formulated as (E2 is the two-body energy and ? is the reduced mass). The zero range model, which is very appropriated to establish the universal laws, is introduced through the ?-Dirac potential. We derive the corresponding two-dimensional Faddeev equations for the three-body system and solve them numerically in momentum space. Our results showed that the three-body binding energy monotonically increases with the two-body binding energy, and such dependence is more pronounced than the mass variations. We found that the three-body energy depends logarithmic on the two-body energy for large values. Furthermore, been m=mB/mA the ratio between the masses of the B and A particles, the three-body energy is mass-independent for m ? ? and increase without bounds for m ?0. The limit of two non-interacting identical particles is also studied in the AAB system. We found that the two-dimensional three-body system always support at least two bound states and more bound states appear for m<0.22. Finally, we analyze the particular limit of m ?0 using the adiabatic approximation. This approximation can be used to study the three-body system in two-dimensions with an accuracy better than 10% compared to the solutions of the Faddeev equations, for m ? 0.01.