## 4 Results and Discussion
First, the radiolytic generation of oxidizing species, such as \({}^{\bullet}\)OH radicals, can trigger oxidative  
Figure 4: Time-dependent extents \(\Delta\)G(H\({}_{2}\)), expressed in molecules per 100 eV, of the main reactions contributing to the generation and decay of H\({}_{2}\) during the radiolysis of pure, de-aerated water by 2 MeV neutrons at 300 \({}^{\circ}\)C (**a**), 350 \({}^{\circ}\)C (**b**), 400 \({}^{\circ}\)C (**c**), 500 \({}^{\circ}\)C (**d**), and 600 \({}^{\circ}\)C (**e**) at 25 MPa, calculated from our Monte Carlo track segment (recoil proton) simulations over the interval of 1 ps to 1 ms. These outcomes indicate that the production of H\({}_{2}\) is largely driven by the oxidation of water by the H\({}^{\bullet}\) atom at higher temperatures, particularly in SCW. stress, potentially leading to the corrosion of materials under supercritical conditions. This affects critical components like fuel cladding, reactor vessels, and other structural elements, vital for maintaining integrity under the high-temperature and high-pressure operating conditions characteristic of these reactors [7, 60, 61, 62]. Second, in conventional pressurized water reactors, adding excess H\({}_{2}\) to the coolant water is a common strategy to suppress net water radiolysis and inhibit the formation of oxidizing radiolytic products (see, e.g., [16, 17, 18, 22, 63, 64, 65]). While it remains uncertain whether this procedure would be equally effective under SCWR conditions [7, 62, 66, 67], the radiolytic formation of H\({}_{2}\) via reaction (9) could impact the minimum concentration of excess H\({}_{2}\), referred to as the 'critical hydrogen concentration', required to prevent the formation of oxidative products from water radiolysis. A few words should be added about our calculated temporal dependence of \(G\)(H\({}_{2}\)O\({}_{2}\)). As is well established, the primary mechanism for H\({}_{2}\)O\({}_{2}\) formation during the track stage of radiolysis is the combination of two \({}^{\bullet}\)OH radicals [10, 13]:  
\[{}^{\bullet}\)OH + \({}^{\bullet}\)OH \(\rightarrow\) H\({}_{2}\)O\({}_{2}\), \(k_{10}\) = 9.87 \(\times\) 10\({}^{9}\) M\({}^{-1}\) s\({}^{-1}\) at 300 \({}^{\circ}\)C.  
At 300 and 350 \({}^{\circ}\)C, within the subcritical water regime, our simulations predict a continuous increase in \(G\)(H\({}_{2}\)O\({}_{2}\)), from an initial value of \(\sim\)0.17 molecule/100 eV to \(\sim\)0.9 molecules/100 eV at 1 ms (see Figure 3e). This temporal evolution resembles that found in previous studies using low-LET irradiation [19], but with higher H\({}_{2}\)O\({}_{2}\) yields, consistent with the high-LET characteristics of fast neutrons. Higher molecular yields are expected due to increased radical-radical reactions at elevated LETs. The slight decrease in \(G\)(H\({}_{2}\)O\({}_{2}\)) when moving from 300 to 350 \({}^{\circ}\)C is explained by the faster diffusion of \({}^{\bullet}\)OH radicals out of the tracks compared to their self-combination within the tracks, resulting in lower H\({}_{2}\)O\({}_{2}\) yields [30, 68]. Unlike in subcritical water, the efficiency of reaction (10) in low-density SCW irradiated at temperatures ranging from 400 to 600 \({}^{\circ}\)C with a pressure fixed at 25 MPa is relatively low. The rate constant for this reaction increases only slightly with temperature, from 1.4 \(\times\) 10\({}^{9}\) M\({}^{-1}\) s\({}^{-1}\) at 400 \({}^{\circ}\)C to 1.5 \(\times\) 10\({}^{9}\) M\({}^{-1}\) s\({}^{-1}\) at 500 \({}^{\circ}\)C, and to 1.9 \(\times\) 10\({}^{9}\) M\({}^{-1}\) s\({}^{-1}\) at 600 \({}^{\circ}\)C [39]. This rate shows significantly less temperature dependence than the diffusion rate of the \({}^{\bullet}\)OH radicals out of the tracks, leading to the expectation of minimal \(G\)(H\({}_{2}\)O\({}_{2}\)) values above the critical point. This outcome, predicted earlier by [PERSON] et al.