Investigation Of Three Body Bound States And Structure Of Rare Gasses

Recently there is been growing interest in few body systems, especially three body systems. In this study our objective is to apply the hyper spherical co-ordinate formulation to three body systems and particularly rare gases, and to calculate the weakly bound states, also our interest is in finding the halo states or Efimov states of realistic atomic or molecular systems and related to the creation of Bose-Einstein condensate.Ultra cold atomic collisions in the experimental or theoretical study and realization of Bose-Einstein condensate system needs to have very weak interactions at very low temperatures and can form a stable bound state. This allows people to study the atomic and molecular weakly bound state.With the invention of quantum mechanics in1920’s and the introduction of Schrodinger equation, it was possible to calculate the atomic structure properties of the atoms. Basic theoretical principles were established with in a decade. But it was not possible or too difficult to solve the atomic structure problem for the even simple atoms. Only simple atom Hydrogen had analytical solution for the energy levels. If we want to calculate the structure and optical properties of any other atom, we have to use some approximation and then solve the resulting Schrodinger equation using different numerical techniques. Since the early times of quantum mechanics, people devolved different numerical methods to solve this problem. With the passage of time, old methods were improved and some new techniques were developed. Invention of electronic computers played an important role in the development of these methods because the techniques which were consider good but were not possible to apply to manual calculations, were revisited and some approximations which were necessary to make the calculations simple at that time, were omitted. So we study different numerical techniques, their comparison and different factors on which the choice of a method is depended to solve the atomic structure problems. We developed computer program based on SVD (Slow variable discretization) to perform bound state calculations for the rare gases three body systems. The He2Ne, He2Ar and He2Kr systems with the combination of the isotopes of the Helium (3He,4He) are used in these calculations. Three-body channel functions and adiabatic potential functions have been calculated using the B-spline method. We use these channel functions in the slow variable discretization (SVD) method to calculate the three-body bound states of the rare gases. Using this method, two bound states for the4He220Ne, and one bound state for each of the4He-3He-20Ne and3He2-20Ne systems have been found.4He240Ar,4He-3He-40Ar and3He240Ar systems have four, three and two bound states respectively. There are four, three and three bound states for4He284Kr,4He-3He-84Kr and3He284Kr systems. Geometry of the trimmers is also analyzed using the probability densities and expectation values, and concluded geometry and average system size is similar for ground states of these trimmers.