Exchange interaction in the yellow exciton series of cuprous oxide

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