## 2 Fast-Neutron Irradiation of Water  
The interactions of neutrons are highly dependent on their kinetic energy (see, e.g., [22; 24; 25]). For 'fast' neutrons, with kinetic energies ranging from \(\sim\)0.5 to 10 MeV, slowing down primarily occurs through multiple successive 'billiard-ball' elastic collisions with atomic nuclei, following the laws of energy and momentum conservation from classical particle physics. During these interactions, a portion of the neutron's kinetic energy is transferred to the nucleus. In fast-neutron radiolysis of water, neutrons are predominantly moderated through interactions with both hydrogen (proton) and oxygen nuclei, creating a spectrum of recoil-ion energies ranging from zero up to the energy of the incident neutrons. These proton and oxygen ion recoils are widely spaced along the neutron path. Their maximum ranges, or track lengths, are considerably shorter than the average distance between two successive neutron interactions. For instance, the mean free path of a 2 MeV incident neutron in water at 25 \({}^{\circ}\)C is about 4 cm, whereas the maximum ranges for recoil protons and oxygen ions at this energy are -75.5 and 1.5 \(\upmu\)m, respectively [25; 26]. Consequently, they can be considered to behave independently of each other. Under normal irradiation conditions (i.e., in the absence of dose-rate effects), their energy is deposited locally within isolated, dense tracks near the neutron collision sites--the points where the recoils are generated--with no overlapping reaction zones from neighboring tracks. As a result, the water radiolysis chemistry observed should be similar to that induced by independent, high 'linear energy transfer' (LET) protons and oxygen ions. This understanding of the track structure underpins the approach used in this work to calculate the radiolysis yields for fast neutrons by simply summing the individual \(G\) values for each of these recoil ions, weighted by their fraction of total neutron energy deposited [13; 25; 27; 28]. In the neutron energy range of interest, oxygen ion recoils play a minor role in the fast-neutron radiolysis of water due to their relatively low average energies. Studies have demonstrated that in light water, proton recoils absorb \(\sim\)93% of the neutron energy, with the remaining energy absorbed by oxygen ions [21; 29]. When calculating radiation chemical yields due to 2 MeV neutrons, we consider only the contributions from the first three recoil protons (i.e., from the first three neutron collisions). After three collisions, subsequent recoil protons have only a negligible impact on radiolysis due to their minimal contribution to the dose (see, e.g., [27; 30]). The 'average' energy loss--important to note, as average values are relevant when dealing with a beam comprising many neutrons--after \(n\) collisions can be determined using the following equation [24; 25; 27]:  
\[\overline{\ln\left(\frac{E_{0}}{E_{n}}\right)}\ =\ n\,\xi \tag{4}\]  
where  
\[\xi\ =\ 1\ +\ \frac{\left(A\ -\ 1\right)^{2}}{2\,A}\,\ln\left(\frac{A\ -\ 1}{A\ +\ 1}\right) \tag{5}\]  
Here, \(A\) refers to the atomic number of the recoil ion. For collisions involving protons, where \(A\) = 1, Equation (5) is not explicitly defined. However, the limit as \(A\) approaches unity is applicable, and in this case, \(\xi\) = 1. Consequently, the average kinetic energy of the neutron after \(n\) individual elastic scattering collisions can be expressed as  
\[E_{n}\ =\ E_{0}\,e^{-n} \tag{6}\]  
where \(E_{0}\) = 2 MeV is the initial kinetic energy of the neutron. Based on this formulation, we can deduce the following initial energies for the three considered protons: \(E_{p_{1}}\) = (\(E_{0}\)-\(E_{1}\)) = 1.264 MeV, \(E_{p_{2}}\) = 0.465 MeV, and \(E_{p_{3}}\) = 0.171 MeV.