  We study the phase space structures that control the transport in a classical
Hamiltonian model for a chemical reaction. This model has been proposed to
study the yield of products in an ultracold exothermic reaction. In the
considered model, two elements determine the evolution of the system: a Van der
Waals force and short-range force associated with the many-body interactions.
In the previous work has been used small random periodic changes in the
direction of the momentum to simulate the short-range many-body interactions.
In the present work, random Gaussian bumps have been added to the Van der Waals
potential energy simulate the short-range effects between the particles in the
system. We compare both variants of the model and explain their differences
similarities and differences from a phase space perspective. In order to
visualize the structures that direct the dynamics in the phase space, we
construct a natural Lagrangian descriptor for Hamiltonian systems based on the
Maupertuis action $S_0$.
