## 2 Materials and Methods (Theoretical Bases and Methods)
The kinetic coefficients of the kinetic equation must be calculated, considering additional elements in the expression of the quantum transparency of a potential barrier perturbed by a polarizing field. These elements were not previously calculated for the parabolic potential barrier [6]. Solutions to the generalized kinetic equation for an external field-perturbed double-symmetric potential well of parabolic form have also not been presented to date. 3. Investigate the phenomenological Bucci-Rive formula for calculating the current density of thermally stimulated depolarization (TSDC), considering additional corrections due to the external electric field and rate of probability of quantum proton transitions through the parabolic potential barrier (for initial polarization). These amendments for the parabolic potential barrier have not been calculated to date. Note that the barrier's parabolic form brings the mathematical model closer to the real spatial structure of the crystal lattice. 4. Analyze the temperature spectra of the thermally stimulated depolarization current density (TSDC) measured by the authors [1,4] for crystals of the HBC class using the example of phlogopite mica, onot talc and muscovite. Identify the physical nature of each experimental maximum and reflect the effect of crystal structure parameters and relaxer parameters (activation energy, equilibrium concentration) on the temperature, position and amplitude of TSDC mono-relaxation maxima. 5. Perform precision measurements of TSCD density temperature spectra for chalcanthite crystals. Analyze the effects of alloying impurities' concentrations and calcination temperatures on the properties and parameters of individual experimental maxima in the TSDC chalcanthite spectrum. No studies have been conducted on the density spectra of TSDC chalcanthite to date. 6. Calculate theoretical TSDC spectra for phlogopite, onot talc, muscovite and chemically pure chalcanthite crystals. Establish the nature of the effects of the design values of the relaxer parameters on the temperature position and amplitude of each individual theoretical maximum in the TSDC density spectrum. Previously, no theoretical TSDC density spectra were calculated for the crystal potential model as a double-symmetric potential well of parabolic shape. * Perform numerical calculations of the parameters of relaxers (activation energy, equilibrium concentration), based on the minimizing comparison function method (MCF-method) [1]. Calculations of relaxer parameters will be carried out over a wide temperature range (50-550 K) and external field parameters (0.1-1 MV/m). * Investigate the effects of tunnel-proton transitions on the low-temperature (50-100 K) and high-temperature (250-550 K) TSDC density maxima properties and relaxer parameters in HBC. Studies on this level of patterns for the double-symmetric parabolic potential pit model have not been conducted to date. * Describe, in the form of chemical equations, the physical mechanism of quantum tunnel proton motion in HBC with a complex crystal structure (layered silicates; crystalline hydrates). To simplify the solution to the kinetic equation, when describing the internal crystal field, we used a double-symmetric potential well [1, 6], which makes it possible to exclude the influence of spatial inhomogeneities in the electric field induced by the dielectric on the kinetics of polarization. Since this paper focuses on the study of proton-tunneling mechanisms and their effect on the contours of theoretical current density graphs, rather than providing a detailed analysis of the electret effect [1], this approach is justified from a physical point of view. The crystal potential relief for protons in HBC is assumed to be one-dimensional \(\mathrm{U}_{C}(\mathrm{x})\), where \(\mathrm{x}\) is the proton coordinate [1].