= &&
            ( c_{1}'^{*} c_{3}^{} + c_{3}'^{*} c_{1}^{} ) I_{n-1,n'-1}(x)
            && - && ( c_{2}^{} c_{4}'^{*} + c_{4}^{} c_{2}'^{*} ) I_{n,n'}(x), \\
    \end{aligned}$$ and this is obtained, of course, using the standard representation of the $ \gamma $-matrices we have chosen. The argument of all Laguerre functions in (\[rad\_alpha\]) is defined as follows: $$x = \frac{1}{2eH} \, k^{2} \sin^{2} \theta.$$ The quantities with and without a dash in (\[rad\_alpha\]) are related to the final and initial state of the electron respectively, and we also use this notation in what follows.

Making the summation over the quantum numbers $ n', s', p' $ characterizing the final state and evaluating the integral over $ k $ in (\[rad\_W\_def\]), one obtains the expression for the radiation power (related to one unit of length of the $ z $-axis): $$\label{rad_W_sum}
    W =
        \sum_{n'} \frac{e^{2}}{2\pi}
        \int \frac
        { k^{2} \sin \theta \, d\theta \, d\varphi }
        { \left|
            1 + \left( \frac{\partial E'}{\partial k} \right)_{n'}
        \right | } \,
        \bar{S}, \qquad
        \bar{S} = \left| {\langle}\bar{{\boldsymbol}\alpha} {\rangle}{\bf f} \right|^{2},$$ where $ k $ and $ p' $ obey the conservation laws of the energy and $ z $-component of the momentum: $$\label{rad_conserv_cond}
    E' = E - 