  We study theoretically the Coulomb interaction between excitons in transition
metal dichalcogenide (TMD) monolayers. We calculate direct and exchange
interaction for both ground and excited states of excitons. The screening of
the Coulomb interaction, specific to monolayer structures, leads to the unique
behavior of the exciton-exciton scattering for excited states, characterized by
the non-monotonic dependence of the interaction as function of the transferred
momentum. We find that the nontrivial screening enables the description of TMD
exciton interaction strength by approximate formula which includes exciton
binding parameters. The influence of screening and dielectric environment on
the exciton-exciton interaction was studied, showing qualitatively different
behavior for ground state and excited states of excitons. Furthermore, we
consider exciton-electron interaction, which for the excited states is governed
by the dominant attractive contribution of the exchange component, which
increases with the excitation number. The results provide a quantitative
description of the exciton-exciton and exciton-electron scattering in
transition metal dichalcogenides, and are of interest for the design of
perspective nonlinear optical devices based on TMD monolayers.
