CHAOTIC SCATTERING THROUGH POTENTIALS WITH RAINBOW SINGULARITIES

We investigate chaotic scattering in a family of two dimensional Hamil tonian systems. The potential in which a point particle scatters consi sts of a superposition of a finite number of central force potentials. Each central force potential is either attracting without any singula rity, or attracting at long distances with a repelling singularity in the center motivated by potentials used in molecular interaction. The rainbow effect obtained from scattering in one such potential causes t he chaotic scattering, and we show that for these systems there exist regions in the parameter space where the repelling sets are complete t wo dimensional Canter sets of different type. We define symbolic dynam ics and calculate periodic orbits for these systems and determine the classical escape rate and the quantum mechanic resonances using the ze ta-function formalism. We examine the systems with two, three, and fou r attracting Gaussian potentials and two Lennard-Jones potentials.