Interactions between Rydberg excitons in Cu$_2$O

Highly-excited states of excitons in cuprous oxide have recently been observed at a record quantum number of up to $n=25$. Here, we evaluate the long-range interactions between pairs of Rydberg excitons in Cu$_2$O, which are due to direct Coulomb forces rather than short-range collisions typically considered for ground state excitons. A full numerical analysis is supplemented by the van der Waals asymptotics at large exciton separations, including the angular dependence of the potential surfaces.