Tunneling of a composite object

The phenomenon of quantum tunneling is relevant in different areas of physics, from chemical reactions to nuclear fission and fusion below the Coulomb barrier. In most of the cases one has to deal with the tunneling of a complex object with internal degrees of freedom. In a one-dimensional model we investigate how an harmonically bound two-body system tunnels through an external gaussian barrier. The hamiltonian in the center of mass (C.M.) and relative coordinates, R and ξ, is