I believe there is Coulomb scattering. However, are there any other channels? Could the products of the reaction be H and H2, and what would be the cross section of this reaction?
You need to consult a correlation diagram for all the channels of H3 and decide whether your reactants are on the singlet or one of the triplet surfaces. You have a charge exchange reaction.
There are many studies of H3 reactions -classical and quantum. So you don't need to do this yourself. You can almost certainly look up the calculated cross-sections for the collision energy of interest to you.
Chapter 8 of the book 'Molecular Potential energy functions' by Murrell et al (J Wiley) discusses the H3 surface but you will need something more recent for charge exchange reactions.