## 3 Results and Discussion
### Hyperfine Interaction Spectroscopy (ESEEM and ENDOR Methods)  
There are several approaches for the analysis of hyperfine interactions that cannot be registered in EPR spectra due to the small value of splitting. This section is dedicated to ESEEM (X-band) and ENDOR (X- and W-band) spectra recorded at the field positions corresponding to the maximum of echo intensity. Taking into account the wide excitation bandwidth of short microwave pulses (approx. 50 MHz) and significant spectra overlapping between signals of different paramagnetic centers, current X-band ENDOR measurements cannot be used to selectively address the paramagnetic centers. Nevertheless, important information can be gathered from the analysis. The crystal lattice of CP samples contains ions with magnetic nuclei (\({}^{1}\)H and \({}^{31}\)P both with \(I=1/2\)). Therefore, if the radiation-induced center is localized near these ions, we can register the corresponding signal of the electron-nuclear interaction. In the spectrum for the X-ray irradiated HA sample (Figure 5a), only signals from phosphorus nuclei (\({}^{31}\)P, \(\
u_{x}\approx 5.9\) MHz at B\({}_{0}=340\) mT) are observed, although the material also contains hydrogen atoms. This result may indicate that for the HA material, the carbonate radical occupies positions near the phosphorus groups PO\({}_{4}\). The ESEEM spectrum of the irradiated OCP sample (Figure 5b) was registered for the nitrate radical at B\({}_{0}=341.8\) mT (see Figure 1a). The ESEEM spectrum contains a complete set of signals from all magnetic nuclei (\({}^{1}\)H, \(\
u_{x}\approx 14.2\) MHz), which indicates the position of the nitrate radical directly in the crystal lattice of the OCP sample. Consequently, in further investigations, the nitrate radical can be successfully used as a spin probe for analyzing the concentration dependences of samples doped with various impurity ions. However, the presence of a sufficiently intense signal from the hydrogen nuclei and the existence of the second harmonic of \({}^{1}\)H (2\(\
u_{x}\)) may indicate the localization of the nitrate radical near the hydrogen layers of OCP. The nitrogen radical in the CP structure can also provide the possibility of using the ENDOR method for a more detailed analysis of the nuclear environment. It is worth noting that due to the insufficient spectroscopic resolution of the method, we could not observe the additional splitting of the lines. In contrast to other methods of measuring hyperfine interactions with neighboring magnetic ligands, the ENDOR method allows for the direct registration of NMR transitions, which significantly increases the spectral resolution. In the ENDOR spectrum of the irradiated OCP with fixed B\({}_{0}=341\) mT, signals at the Zeeman frequencies corresponding to protons (\(\
u_{x}\approx 14.8\) MHz) and phosphorous \({}^{31}\)P (\(\
u_{x}\approx 5.9\) MHz) nuclei are observed (Figure 6). Only one broad signal for \({}^{31}\)P is detected, which can be simulated as a convolution of Gaussian and Lorentzian lines with the line widths of 1.6 MHz and 0.4 MHz; however, in HA, a \({}^{31}\)P splitting of 0.5-1.0 MHz can be observed [35; 36; 58]. The absence of well-structured ENDOR and ESEEM signals from phosphorous and hydrogen nuclei may be explained by the irregularity of the incorporation of several distinct (R1-R3) defects [54] into the lattice (it is either because of preferential localization in the disordered hydrated layer or due to a large variety of incorporation sites in the apatite layer). Most probably, in