Anisotropic two-body problem under the Buckingham potential

We present a qualitative study of the dynamics of two-point masses interacting via an anisotropic generalized Buckingham potential. We describe the asymptotic behaviour of escape orbits and prove that set of initial conditions of the escape orbits has a non-zero phase-space volume. We also apply the Melnikov method to show that the flow on the zero energy level set of the negatively charged anisotropic generalized Buckingham problem is chaotic.