Photoelectrons and secondary electrons have recently been observed to have been reflected back to the ATS 6 spacecraft from a potential barrier in the spacecraft vicinity. Guernsey and Fu (1970) and others have predicted the presence of a potential barrier in a photoelectron sheath. In order to determine whether or not he observed barrier is due to the emitted electrons, a theory for a spherically symmetric sheath has been developed which includes the effects of both the emitted electrons and the ambient plasma electrons and ions. A thick sheath approximation based on an analysis of particle tracjectories in phase space is obtained which is valid for large particle Debye lengths. A comparison with the ATS 6 data shows that the observed barrier potentials are too large to be explained in this way.