Gaussian peaks, 1 -4 each of them spreading about (and possibly characterized by) a central, well-defined depth.These discrete depths coincide with the trap-depths given by the "glow-curves" method, but this last method is not accurate enough to show the existence of distributions around these depths.The study of the decay at different temperatures gives the same depths, and this provides a direct verification of the above fundamental formula.This agreement between theory and experiment may be considered as a proof of the monomolecular mechanism involved. Precise experiments are indeed not consistent with the hyperbolic decay law, which is deduced, as is well known, from the assumption of a bimolecular mechanism. However, the derivation of the 1/P law implies also the assumption that there is a unique trap depth, 5 and the discrepancy may, at first sight, be attributed to this over-simplification. I have shown that for long times of decay the l/fi law should then be obtained whatever the distribution of traps may be, and so the discrepancy between the results and the bimolecular mechanism is actual.Thus the experiments are consistent with a monomolecular decay, at least as a first approximation. This may be explained if a great number of traps are situated in the neighborhood of the activator centers. But the existence of photoconductivity and recapture implies the possibility of a more or less important bimolecular perturbation. The above results show that this perturbation is weak during the decay.If the electrons in the conduction band have high energies, they are not stopped by the defects of the crystal, and in these conditions an approximately bimolecular mechanism is valid; this is the case if excitation or stimulation takes place, or if the electrons are accelerated by an electric field; it may also be the case during the first stage of the decay 6 (10 -2 sec), when the electrons in the conduction band are coming out of very shallow traps. However, during the long-period phosphorescence caused by the release of electrons from deeper traps, the conduction electrons have very low energies because of the need of a thermal activation (wave mechanical calculations 7 show that these energies are less than kT). They cannot then go far from the traps, and they often fall into the next center, in agreement with an approximately monomolecular decay.Even in this case of monomolecular decay, however, retrapping takes place if different traps are situated around the same center; the possibility of a bimolecular perturbation also involves recapture. I have studied theoretically the way in which the decay depends on this phenomenon. Analogies appear between the refilling of shallow traps by electrons escaped from deeper traps, and chains of successive radioactive disintegrations. For instance, the quick decay of the glow curves obtained when the time elapsed after the end of the excitation increased is not an evidence against recapture, exactly as the activity of a mixture containing comparable weights of radium and rad...