  We experimentally and numerically investigate the exchange interaction of the
yellow excitons in cuprous oxide. By varying the material parameters in the
numerical calculations, we can interpret experimental findings and understand
their origin in the complex band structure and central-cell corrections. In
particular, we experimentally observe the reversal of the ortho- and
paraexciton for the $2S$ yellow exciton, and explain this phenomenon by an
avoided crossing with the green $1S$ orthoexciton in a detailed numerical
analysis. Furthermore, we discuss the exchange splitting as a function of the
principal quantum number $n$ and its deviation from the $n^{-3}$ behavior
expected from a hydrogenlike model. We also explain why the observed exchange
splitting of the green $1S$ exciton is more than twice the splitting of the
yellow $1S$ state.
