Neutron-activation revisited: The depletion and depletion-activation models

The growth of a radioactive daughter in neutron activation is commonly described with the saturation model that ignores the consumption of parent nuclei during the radio-activation process. This approach is not valid when radioactive sources with high specific activities are produced or when the particle fluence rates used are very high. Assuming a constant neutron fluence rate throughout the activation target, a neutron-activation model that accounts for the depletion in parent nuclei is introduced. This depletion model is governed by relationships similar to those describing the parent-daughter-granddaughter decay series, and, in contrast to the saturation model, correctly predicts the practical limit of the daughter specific activity, irrespective of the particle fluence rate. Also introduced is a neutron-activation model that in addition to parent depletion accounts for the neutron activation of daughter nuclei in situations where the cross section for this effect is high. The model is referred to as the depletion-activation model and it provides the most realistic description for the daughter specific activity in neutron activation. Three specific neutron activation examples of interest to medical physics are presented: activation of molybdenum-98 into molybdenum-99 described by the saturation model; activation of cobalt-59 into cobalt-60 described by the depletion model; and activation of iridium-191 into iridium-192 described by the depletion-activation model.