## 3 Results and Discussion  
Figure 4 illustrates microdosimetric frequency distributions, represented as \(yf(y)\), acquired under different boron concentrations and in the absence of boron. The left panel employs a logarithmic \(x\)-axis and a linear \(y\)-axis, ensuring that equivalent visual areas under the curves signify identical relative contributions to the total number of events. Notably, around half of the events exhibit lineal energy values below 0.15 keV/\(\upmu\)m, with a minimal fraction surpassing 20 keV/\(\upmu\)m. Specifically, this fraction is less than 0.1% without \({}^{10}\)B and rises to nearly 0.3% at a 100 ppm \({}^{10}\)B concentration. When examining \(yf(y)\) on a linear scale, the spectra with or without \({}^{10}\)B exhibit almost indistinguishable patterns, primarily due to the minor proportion of neutron-capture events involving boron compared to the total events. In the right panel of Figure 4, a double logarithmic scale is employed to accentuate small distinctions in events occurring above approximately 20 keV/\(\upmu\)m. These variations arise from the increasing occurrence of BNC events as the boron concentration increases. Notably, the spectra maintain a consistent shape in the photon region (below 20 keV/\(\upmu\)m), indicating minimal additional gamma components introduced by boron doping. This confirms the validity of the adopted procedure for aligning the photon components. Figure 5 illustrates the dose distributions of the lineal energy at different boron concentrations. The distributions are graphed as \(yd(y)\) vs. \(y\), with the lineal energy \(y\) represented on a logarithmic scale. This graphical representation ensures that the size of the area under the curve between any two \(y\) values corresponds to the dose fraction in that range. In the left panel of Figure 5, the \(d(y)\) distributions are individually normalized to a unit dose, following the definition of the dose probability density of \(y\), denoted as \(d(y)\)[22]. As the high lineal energy components increase in the boronated spectra, the corresponding gamma components decrease to maintain normalization. It is important to note that this misalignment of the photon regions does not imply a reduction in gamma doses; instead, the gamma doses are expected to remain nearly the same. To address this, the photon regions (i.e., the part of the spectra below approximately 20 keV/\(\upmu\)m) of the boronated spectra are aligned with the distribution without \({}^{10}\)B by scaling them with constant factors. This scaling, crucial for matching the gamma components, is a necessary step to accurately assess the additional contribution to the dose resulting from the boron neutron capture  
Figure 4: Frequency distributions of lineal energy with varying \({}^{10}\)B concentrations. (**a**) The logarithmic \(x\)-axis and a linear \(y\)-axis representation ensures that equal visual areas under the curves correspond to equal relative contributions to the total number of events; (**b**) the logarithmic vertical axis highlights variations in the spectrum’s rightmost portion associated with the BNC reaction. Figure 5: Dose distributions of lineal energy measured with different concentrations of \({}^{10}\)B. (**a**) All distributions have been normalized to a unit dose; (**b**) the dose distribution without \({}^{10}\)B is normalized to the unit dose, while the other distributions are scaled to align their gamma components, below 10 keV/\(\upmu\)m, with the distribution without \({}^{10}\)B.  
reaction. Following proper scaling, the process enables the derivation of the pure BNC component by subtracting the boron-free spectrum from the one with boron. As a result, the scaled \(d(y)\) distributions for the boronated scenarios lose normalization. The excess beyond the unit dose, in the high-\(y\) region, reflects the dose fraction enhancement attributable to boron neutron capture reaction products.