An essentially exact many body calculation for muonic molecular ions and exotic coulombic systems

The L = 0 bound states and the structural properties of muonic molecular ions and exotic nuclear molecular ions are calculated by a hyperspherical harmonics expansion method, which is an essentially exact method for three-body systems. We examine the convergence rate of this method and also examine its crucial dependence on the mass ratio ? (ratio of the masses of similar to dissimilar particles). An a priori criterion for the rate of convergence and the required size of the expansion basis for a predetermined precision have been suggested. Our calculation reveals the cluster type of structure of these systems.