Chaotic scattering through potentials with rainbow singularities

We investigate chaotic scattering in a family of two dimensional Hamiltonian systems. The potential in which a point particle scatters consists of a superposition of a finite number of central force potentials. Each central force potential is either attracting without any singularity, 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 the chaotic scattering, and we show that for these systems there exist regions in the parameter space where the repelling sets are complete two dimensional Cantor sets of different type. We define symbolic dynamics and calculate periodic orbits for these systems and determine the classical escape rate and the quantum mechanic resonances using the zeta-function formalism. We examine the systems with two, three, and four attracting Gaussian potentials and two Lennard-Jones potentials.