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We study conceptional problems of a photo-electron emission (PEE) processfrom a free exciton in insulating crystals. In this PEE process, only theelectron constituting the exciton is suddenly emitted out of the crystal, whilethe hole constituting the exciton is still left inside and forced to berecoiled back to its original valence band. This recoil on the hole is surelyreflected in the spectrum of the PEE with a statistical distribution along themomentum-energy curve of the valence band. This distribution is nothing but thesquare of the exciton wave function amplitude, since it shows how the electronand the hole are originally bound together. Thus, the momentum-resolved PEE candirectly determine the exciton wave function. These problems are clarified,taking the $\Gamma$ and the saddle point excitons in GaAs, as typical examples.New PEE experiments are also suggested.

Direct Determination of Exciton Wave Function Amplitudes by the Momentum-Resolved Photo-Electron Emission Experiment