How is the electron "trapped in the crystal" in irradiated NaCl? Pennsylvania State University provides irradiated $\ce{NaCl}$ (180,000 rads of gamma radiation) to teachers for a very entertaining demonstration. The salt is orange after irradiation. When it is placed on a hot plate, you see a flash of visible light and the salt returns to it normal color. The explanation provided with the salt is that "The heat allows the electrons that were trapped in the crystal structure (when the energy was deposited) to return to their original position." This language evokes a picture of a particle electron in a crystal jail for me. The explanation goes on to say that the energy is released as a photon of visible light. (I understand this part of the explanation.) So, my question is, how are electrons trapped in a crystal structure? What keeps them in an excited state?
What you're describing is thermoluminescence, which is used as a paleochronology method (aka Trapped Electron (TE) dating, afaik). The wikipedia article has a good synopsis. Simply, electrons get bound to potential wells generated in the radiation-defected structure. When you heat the crystal up you allow it to anneal and return to a more regular structure. The defected crystal is stuck in an energetic local minimum.

You can also do this trick with X-rays. Calcite (or was it aragonite?) exposed to X-rays will turn light blue for a while.