  We analyze theoretically the Coulomb scattering processes of highly excited
excitons in the direct bandgap semiconductor quantum wells. We find that
contrary to the interaction of ground state excitons the electron and hole
exchange interaction between excited excitons has an attractive character both
for $s$- and $p$-type 2D excitons. Moreover, we show that similarly to the
three-dimensional (3D) highly excited excitons, the direct interaction of 2D
Rydberg excitons exhibits van der Waals type long-range interaction. The
results predict the linear growth of the absolute value of exchange interaction
strength with an exciton principal quantum number, and point the way towards
enhancement of optical nonlinearity in 2D excitonic systems.
