## 3 Results
### Dielectric Loss Tangent
According to experiments in the HBC, particularly in the crystals of chalcanthite, phlogopire, muscovide, and talc, with an experimental sample thickness of d = 30 microns (in the region of the high-temperature maximum of the thermally stimulated depolarization current (near T \(\approx\) 150-550 K)), the measured equilibrium concentrations of the main charge carriers (protons) exhibit sufficiently high values (in comparison with the region of low temperatures \(n_{0}\approx(10^{16}\div 10^{17})\,\text{m}^{-3}\)) and make up \(n_{0}\approx(10^{18}\div 10^{21})\,\text{m}^{-3}\). High-frequency dielectric constants for the HBC are taken to be equal to \(\varepsilon_{\infty}\approx(1\div 10)\). Furthermore, via the results of calculations, we obtain \(\text{T}_{A}=1.9138\cdot(10^{3}\div 10^{7})\) K, and at T \(\approx(1.5-5.5)*10^{2}\) K, we have \(\frac{\text{T}}{\text{T}_{A}}\approx(0.7838\div 2.8737)\cdot(10^{-5}\div 0.1)\). Since the kinetic coefficients (133) and (134) are in the temperature range T \(\approx\) 150-550 K, according to the experiment, in the case of the HBC, they should be calculated at activation energies \(\text{U}_{0}\approx(0.1-1.0)\) eV, when proton hydrogen bond transitions are realized mainly via thermal activation and, accordingly, at T \(\approx(1.5-5.5)*10^{2}\) K when the approximate ratio \(\frac{W^{(0)}(\text{T})}{W^{(1)}(\text{T})}\approx 1\). The values of the shielding radius \(\frac{\text{r}_{\rm D}(\text{T})}{\text{d}}\approx\Big{(}0.28\times 10^{-2}-0.536\Big{)}\) in the confidence interval of the measured values of the parameters \(n_{0}\) and \(\text{U}_{0}\) are fully consistent with the conditions of Maxwell relaxation. These conditions are \(\frac{T_{\rm D}(\rm T)}{T_{\rm M}(\rm T)}>1\), \(\frac{\rm T}{T_{A}}<1\), and \(\frac{T_{\rm D}(\rm T)}{\rm d}<1\). For calculations of the Debye radius of the volume charge shielding in the low-temperature maximum area of thermostimulated depolarization currents in relation to the HBC, it is necessary to take into account the quantum tunneling influence of protons on kinetic coefficients (133) and (134) when separating the temperature regions of the tunnel (\(\rm T<T_{cr,move}\)) and thermally activated (\(\rm T>T_{cr,Move}\)) proton transitions due to sufficiently high statistically averaged quantum transparency values of the potential barrier for protons near the critical temperature \(\rm T_{cr,move}=\frac{h_{\rm y}\gamma T_{0}}{\pi T_{0}k_{\rm Ry}\sqrt{m}}\)[8]. In this model, m is the mass of the proton. From the analysis of the experimental spectra of the density of TSTD crystals of the HBC class, particularly natural phlogine \(\rm Mg_{3}(\rm ASi_{4}O_{10})(OH)_{2}\) at \(\rm T_{max,exp,1}=100\) K, \(\rm U_{0,exp,1}=0.05\pm 0.01\) eV; \(\rm talc\)\(\rm Mg_{3}(\rm Si_{4}O_{10})(OH)_{2}\) at \(\rm T_{max,exp,2}=86\) K, \(\rm U_{0,exp,2}=0.06\pm 0.01\) eV; muscovite \(\rm KAl_{2}(\rm AlSi_{3}O_{10})(OH)_{2}\) at \(\rm T_{max,exp,3}=105\) K, \(\rm U_{0,exp,3}=0.04\pm 0.01\) eV; and chemically pure chalcanthite \(\rm CuSO_{4}\)\(\rm 5H_{2}O\) at \(\rm T_{max,exp,4}=94\) K, \(\rm U_{0,exp,4}=0.07\ \pm\ 0.01\) eV, within the vicinity (on the set of points of the continuum measure), the numerical values of the low-temperature maxima are determined, and the corresponding numerical values of the critical temperature \(\rm T_{cr,move}\) within the range from 80 K to 150 K are set.