the classical trajectory of particle. Indeed,one can neglect by the value of commutators $|[\hat{p}_{\perp i}, \varrho_j]|=\delta_{ij}$ comparing with the value $p_{\perp} \varrho$ in this interval ($p_{\perp} \varrho
\geq m\varrho_0 \gg 1$). In this case the expression for the probability has the form (see [@BKS3], Eqs.(7.3) and (7.4)) $$dw = |M(\mbox{\boldmath$\varrho$})|^2w_r({\bf r_{\perp}})d^2
r_{\perp} d^3k,
\label{3.1}$$ where $$M(\mbox{\boldmath$\varrho$})=\frac{e}{2\pi\sqrt{\omega}}\int_{-\infty}^{\infty}
R(t)\exp(ik'x(t))dt,\quad k'=\frac{\varepsilon}{\varepsilon'}k.
\label{3.2}$$ Here $w_r({\bf r_{\perp}})d^2 r_{\perp}$ is the probability to find the emitting particle with the impact parameter $\mbox{\boldmath$\varrho$} = {\bf r}_\perp -{\bf x}$ in the interval $d^2 \varrho = d^2 r_{\perp},~ R(t)=R({\bf p}(t)),~
kx(t)=\omega t-{\bf kr}(t)$ (for details see [@BKS3], Sec. 7.1). Integrating by parts in the last equation and taking into account that $|{\bf q}_{\perp}(\mbox{\boldmath$\varrho$})| \leq
1/\varrho_0 \ll m$ we find $$M(\mbox{\boldmath$\varrho$}) \simeq \frac{i e}{2\pi
\sqrt{\omega}}\int_{-\infty}^{\infty}
\exp(ik'vt)\frac{d}{dt}~\frac{R(t)}{k'v(t)}dt \simeq \frac{i
e}{2\pi \sqrt{\omega}} {\bf m}(\mbox{\boldmath$\varrho$})
\frac{\partial}{\partial {\bf p_{\perp}}} \frac{R({\bf
p_{\perp}})}{k'v}, \label{3.3}$$ where $$\begin{aligned}
&&{\bf p}_{\perp}={\bf p}-{\bf n}({\bf n}{\bf p}) \simeq
\varepsilon ({\bf v}-{\bf n}),
\nonumber \\
&& {\bf m}(\mbox{\boldmath$\varrho$}) = \int_{-\infty}^{\infty}
\exp(ik'vt)\dot{{\bf q}}(\mbox{\boldmath$\varrho$}, t) dt =
-\frac{\partial}{\partial \mbox{\boldmath$\varrho$}}
\int_{-\infty}^{\infty}
\exp\left(\frac{it}{l_f}\right)V(\sqrt{\varrho^2+t^2})dt
\nonumber \\
&& = \frac{2\alpha}{l_f}
\frac{\mbox{\boldmath$\varrho$}}{\varrho}K_1(\frac{\varrho}{l_f})=2\alpha
q_{min} \zeta K_1(\varrho q_{min} \zeta)
\frac{\mbox{\boldmath$\varrho$}}{\varrho},
\label{3.4}\end{aligned}$$ for the Coulomb potential, $K_1(z)$ is the modified Bessel function (the Macdonald function), $R({\bf p_{\perp}})$ has a form of matrix 