Calculations of2p-Exciton States in Semiconductors with Degenerate Bands

Using a method previously introduced to treat $s$ states, we analyze the $2p$-excited states of direct excitons in semiconductors. The splitting of the four $2p$ levels, due to the degeneracy of the valence bands, are given by simple analytical expressions. The symmetry of these levels are discussed for the zinc-blende, diamond, and NaCl structures. Results are given for all semiconductors for which the valence-band parameters are known. Since the actual experimental situation is poor, suggestions are made as to which substances should be investigated in order to appreciate these splittings.