Studtite [(UO$_2$)(O$_2$)(H$_2$O)$_2$]·2(H$_2$O) is a secondary phase precipitating during the alteration of uranium-bearing materials. The mechanistic link between the formation of uranyl and peroxide bonds in the solid and the nature of the oxidizing species produced by water radiolysis remains to be elucidated. In order to improve our understanding of these mechanisms, an original experimental methodology in the presence of $^{18}$O isotopes and Raman spectroscopy has been developed. It appears that there is a direct chemical relationship between the peroxo ligands inside studtite and the peroxide entities of H$_2$O$_2$ molecule into the solution. The link between H$_2$O$_2$ formation mechanism in solution by the radiolysis of water, the nature of the radiation and the isotopy of the peroxo ligands inside studtite has been described thanks to a coherent set of experimental data. For the uranyl UO$_2$$^{2+}$ ions, the characterization of its isotopy allows to specify the mechanism of oxidation at the UO$_2$ /water interface. The isotopic configurations observed for the uranyl ion inside studtite, can be explained by assuming an oxidation mechanism of UO$_2$ involving both a simple transfer of electrons by interaction with H$_2$O$_2$ and the incorporation of oxygen atoms from the solution into the fluorite structure via OH° radicals.