On The E:x:citon Problem m Insulating Crystals

The general probl ~ of configuration interacti~ns for.the excited states in ideal insulators is in-vestigated by solving a d.ifference equation which is derived in the same way as in the scattering problem; It is ~hown that the general picture of exciton falls into three categories: deep case, shallow case, and hydrogenic ca:se, according to different conditions tinder which the difference equation is to be solved approximately. The structures of the bands of both the singlet and triplet excitons are investigated in these three cases, with particular emphasis on the deep case. The solution derived is intermediate between the " atomic " and "continuum " models hitherto proposed