## 1 Introduction
### Basic Principles of Quasi-Classical Model of Ion Relaxation Polarization
For a discrete range of energy \(\frac{\big{|}E_{n\pm 1,n}\big{|}}{\mathrm{k}\mathrm{g}\mathrm{T}}>1\), \(D^{(0)}(E_{\mathrm{n}})=\exp\left(-\frac{\pi\delta_{0}\sqrt{\mathrm{m}}( \mathrm{U}_{0}-E_{\mathrm{n}})}{\hbar\sqrt{2}\mathrm{U}_{0}}\right)\), in the case of \(E_{\mathrm{n}_{\mathrm{min}}}\leq E_{\mathrm{n}}\leq E_{\mathrm{n}_{\mathrm{ max}}}\), we accept a model of the linear harmonious \(E_{\mathrm{n}}=\hbar\omega_{0}\Big{(}\mathrm{n}+\frac{1}{2}\Big{)}\) for which \(E_{\mathrm{n}_{\mathrm{min}}}=E_{0}=\frac{1}{2}\hbar\omega_{0}\) and \(E_{\mathrm{n}_{\mathrm{max}}}\leq\mathrm{U}_{0}\), and \(\mathrm{n}_{\mathrm{max}}\approx\frac{\frac{\mathrm{U}_{0}}{2}-1}{2}\). Similarly, in the WKB approximation, for the model of a crystalline potential pattern with potential rectangular barriers [1], we have \(D^{(0)}(E)=\exp\left(-\frac{2\delta_{0}\sqrt{2\mathrm{m}(\mathrm{U}_{0}-E)}}{ \hbar}\right)\) in the case where \(0\leq E\leq\mathrm{U}_{0}\) (for a continuous stationary energy spectrum of relaxers) and \(D^{(0)}(E_{\mathrm{n}})=\exp\left(-\frac{2\delta_{0}\sqrt{2\mathrm{m}(\mathrm{ U}_{0}-E_{\mathrm{n}})}}{\hbar}\right)\) in the case of \(E_{\mathrm{n}_{\mathrm{min}}}\leq E_{\mathrm{n}}\leq E_{\mathrm{n}_{\mathrm{ max}}}\) for a discrete spectrum of particle energies, while, in the case of an isolated rectangular potential well, we take the expression \(E_{\mathrm{n}}=\frac{\hbar^{2}\pi^{2}}{2\pi^{2}}\Big{(}\mathrm{n}+\frac{1}{2} \Big{)}^{2}\), where \(a\) is the width of the potential well. The most numerically convenient form of expression (4) is expressed as in [65,69,70,71]  
\[\text{SO}_{4}\text{H}^{-}\to\text{HSO}_{4}^{-}.\]2  
Calculations of the parameter \(\big{|}\Delta\mathrm{U}_{\mathrm{i}\mathrm{j}}(\mathrm{x};\mathrm{t})\big{|} =\frac{\mathrm{qE}_{\mathrm{i}}(\mathrm{x}\mathrm{t})\mathrm{q}}{2}\) are carried out by means of an approximation in which the electric field strength in the crystal \(\mathrm{E}_{\mathrm{i}}(\mathrm{x};\mathrm{t})\) is taken to be a spatially inhomogeneous non-stationary function calculated in this mathematical model near an arbitrary equilibrium state \(\mathrm{x}_{\mathrm{i}}\). In general, we substitute the expansion into an infinite power series:  
\[\text{SO}_{4}\text{H}^{-}\to\text{HSO}_{4}^{-}.\]3  
\[\text{SO}_{4}\text{H}^{-}\to\text{HSO}_{4}^{-}.\]4  
An evaluation of the quasi-classical quantum transparency of the potential barrier \(\mathrm{U(x)}\) perturbed by an electric field is carried out by approximating a weak influence of the spatial inhomogeneity of the field \(\mathrm{E}_{\mathrm{i}}(\mathrm{x};\mathrm{t})\) on the barrier height value \(\frac{\big{|}\Delta\mathrm{U}_{\mathrm{i}\pm 1}\big{|}}{\mathrm{U}_{0}}\ll 1\). Then, \(D^{(\pm)}(\mathrm{U}_{0}\pm|\Delta\mathrm{U}_{\mathrm{i}\pm 1}|;E)=\exp\left(-2 \eta^{(\pm)}(|\Delta\mathrm{U}_{\mathrm{i}\pm 1}|;E)\right)\) is calculated for the local potential \(\mathrm{U}_{\mathrm{i}\pm 1}^{(\pm)}(\mathrm{x};\mathrm{t})=\mathrm{U}( \mathrm{x})\pm|\Delta\mathrm{U}_{\mathrm{i}\pm 1}|\), where, upon integration,  
\[\text{SO}_{4}\text{H}^{-}\to\text{HSO}_{4}^{-}.\]5  
and the parameter \(|\Delta\mathrm{U}_{\mathrm{i}\pm 1}|=\frac{\mathrm{qE}_{\mathrm{i}}(\mathrm{x} \mathrm{t})\mathrm{q}}{2}\) is calculated only in the time function. The same is true for calculating the coordinates of the pivot points for the particle \(\mathrm{U}_{\mathrm{i}\pm 1}^{(\pm)}(\mathrm{x};\mathrm{t})=E\). Computation of the statistically averaged (by energy levels \(E\)) quantum transparency \(D^{(\pm)}(|\Delta\mathrm{U}_{\mathrm{i}\pm 1}|;\mathrm{T})=\Big{\langle}D^{(\pm)}(| \Delta\mathrm{U}_{\mathrm{i}\pm 1}|;E)\Big{\rangle}\) of a parabolic potential barrier perturbed by an external field \(\mathrm{U}_{\mathrm{i}\pm 1}^{(\pm)}(\mathrm{x})=\mathrm{U}_{0}\Big{(}1-\frac{4\kappa^{2}}{8_{0}^{2}} \Big{)}\pm|\Delta\mathrm{U}_{\mathrm{i}\pm 1}|\), in the case of a continuous spectrum of stationary energies of relaxers (ions), is feasible according to quasi-classical statistical theory, relying on the following expression [65; 67; 69; 70; 71]:  
\[