How does radiation facilitate the formation of tetravalent iron? In reading the article abstract What Oxidation State of Iron Determines the Amethyst Colour?, the author states that in regards to the gemstone amethyst, from clear quartz:


  The crystal was transformed into violet amethyst by gamma-irradiation. The change in colour was accompanied by changes in the Mössbauer spectrum that can be interpreted as the conversion of trivalent iron into the tetravalent state: $\ce{Fe^{3+}→Fe^{4+}}$


How does gamma radiation facilitate the conversion of oxidation state of iron, from $\ce{Fe^{3+}}$ to $\ce{Fe^{4+}}$?
The ionization energy of $\ce{Fe^3+}$ to $\ce{Fe^4+}$ is 54.8 eV.
The energy of typical gamma radiation is much higher (in the order of roughly some keV to a few MeV). Depending on the energy, the interaction of average gamma radiation with the affected electron is mainly due to Compton scattering.