polarization (or spin) operator $$\label{sol_Pi_def}
    \hat{\Pi} =
        \Pi_{\bot} \cos \delta + \Pi_{\|} \sin \delta,$$ where $$\Pi_{\bot} = m {\bf \Sigma} + i \gamma^{0} \gamma^{5} [{\bf \Sigma} \times {\bf P}], \qquad
    \Pi_{\|} = {\bf \Sigma} {\bf P},$$ which can be diagonalized together with $ H_{\rm D} $; it is defined in an unambiguous way (when $
\tilde{\mu} \neq 0 $). This operator can be named a “mixed” spin operator since it is a superposition of the well-known transversal $ \Pi_{\bot} $ and longitudinal $ \Pi_{\|} $ polarization parts with the coefficients $ \cos \delta $ and $ \sin \delta $ respectively (for the properties of the electron spin operators see, e.g., [@book_rel_el], [@book_hep_rad]). In the expression (\[sol\_Pi\_values\]) $ n $ is the principal quantum number; it can be easily proved that the corresponding integral of motion is $ {\left( \alpha_{1} P_{1} + \alpha_{2} P_{2}
\right)}^{2} $ with the eigenvalues $ 2eHn $. In the case of $ n = 0 $, the sign of $ \Pi $ (i.e., the spin orientation) as it follows from (\[sol\_Pi\_values\]) takes a definite value. When $
\delta \neq 0 $ it depends on $ p $ (through $ \tilde{m} $, according to (\[sol\_mpeff\_def\])). Besides, it 