The quantum three-body problem plays an important role in different branches of the modern physics. In the nuclear, atomic and molecular physics there exist a number of systems whose behaviour is naturally described in this framework.Both bound states and scattering processes in three-body systems are of great theoretical and experimental importance.
In this thesis an unified approach for a study of three-body systems is suggested.It consists of the total angular momentum representation for the wave function, the exterior complex scaling method and the three-dimensional finite element method.This combination forms a mathematically rigorous and computationally precise and effective approach to treat three-body problems and gives a possibility to calculate various systems from different field of physics.
The recently discovered antiprotonic helium system provides an unique example of relatively long co-existence of matter and antimatter. Also, it is one of very few three-body systems where very accurate experimental data are available. It is unusual from theoretical point of view as it possesses very high angular momentum, up to 40, and shares both properties of molecular and atomic systems. In this thesis we present calculation of energy levels, transition wavelengths, and lifetimes for both the 3He and the 4He isotopic species of the antiprotonic helium.
The normal helium atom is a good test case for any method as a lot of very accurate experimental and theoretical results are available. Calculations of doubly excited states in helium are presented. The results clearly illustrated the preciseness of the present approach.
Another implementation is found in the nuclear physics. It is shown how angular dependent interactions, which are typical for nuclear physics problems, can be incorporated in the formalism. The test case of the halo nucleus 11Li is investigated. In the molecular physics, the weakly bound van der Waals complex NeICl is considered, and its bound states and resonances are computed.
Stockholm: Stockholm University , 1999. , 31 p.
Three-body problem, Total angular momentum representation, Resonances, Complex Scaling Method, Finite Element Method, Eigenvalues problem.