Simple potential model for interaction of dark particles with massive bodies

A simple model for interaction of dark particles with matter based on resonance behavior in a three-body system is proposed. The model describes resonant amplification of effective interaction between two massive bodies at large distances between them. The phenomenon is explained by catalytic action of dark particles rescattering at a system of two heavy bodies which are understood here as the big stellar objects. Resonant amplification of the effective interaction between the two heavy bodies imitates the increase in their mass while their true gravitational mass remains unchanged. Such increased interaction leads to more pronounced gravitational lensing of bypassing light. It is shown that effective interaction between the heavy bodies is changed at larger distances and can transform into repulsive action. (paper)