Effect of molecular oxygen on the formation of radicals in irradiated polymethyl methacrylate

A mathematical problem which relates the instantaneous oxygen concentration to the formation of radiation induced radicals in polymethyl methacrylate is rigorously solved. Based on this result, first, the validity of an apparent threshold dose for radical formation, was proved; second, the interaction constant between oxygen molecules and the radicals was calculated explicitly. (Dosimetry, Radiation induced radicals. Oxygen effect on radical formation).