<{\bf q}^2(\mbox{\boldmath$\varrho$})>-<{\bf
q}(\mbox{\boldmath$\varrho$})>^2 \propto \left< \frac{1}{({\bf
x}_0+\mbox{\boldmath$\varrho$})^2}-\frac{1}{{\bf x}_0^2}\right>
\nonumber \\
&& \simeq \left< \frac{4({\bf x}_0
\mbox{\boldmath$\varrho$})^2}{{\bf
x}_0^6}-\frac{\mbox{\boldmath$\varrho$}^2}{{\bf x}_0^4}\right> =
\frac{<\mbox{\boldmath$\varrho$}^2>}{{\bf
x}_0^4}=\frac{2\sigma^2}{{\bf x}_0^4}.
\label{5.17}\end{aligned}$$ Substituting (\[5.16a\]) into Eq.(\[5.7\]) and multiplying the result by the luminosity (\[4.3\]): $${\cal L}=N_c N_r\frac{\Sigma^2}{\pi}\exp(-{\bf x}_0^2 \Sigma^2)
 \label{5.18}$$ we have for the probability of bremsstrahlung of round beams moving apart at large distance $$\begin{aligned}
&&dw_{\gamma} \simeq 4N_c
N_r\frac{\alpha^3}{\pi}\lambda_c^2\Sigma^2
\frac{\varepsilon'}{\varepsilon}\frac{d\omega}{\omega}\left(
v-\frac{2}{3} \right)
\nonumber \\
&& \times\left[ \exp(-{\bf x}_0^2 \Sigma^2) \ln \frac{m}{\Sigma}+
\frac{\sigma^2\Sigma^2}{({\bf x}_0^2\Sigma^2)^2}+O(\exp(-{\bf
x}_0^2 \Sigma^2))\right]
\nonumber \\
&& \Sigma^2=\frac{1}{2(\Delta^2+\sigma^2)},\quad  {\bf x}_0^2
\Sigma^2=\frac{z_0^2+y_0^2}{2(\Delta^2+\sigma^2)} \gg 1, \quad
q_{min}^2(z_0^2+y_0^2) \ll 1.
\label{5.19}\end{aligned}$$ According to (\[5.19\]) when ${\bf x}_0^2$ increases so that one can neglect the first term in square brackets, the probability of bremsstrahlung of the round beams diminishes as a power of distance between beams ($\propto \sigma^2/{\bf x}_0^4$). The cross section Eq.(\[5.7\]) in this case grows exponentially as $e^d/d^2$. Let us note that without the subtraction term one has erroneous qualitative behaviour of probability ($\propto 1/{\bf
x}_0^2$). These circumstances explain also Eq.(\[5.12\]) for the coaxial beams: at integration over $d^2\varrho$ the region contributes where $<{\bf q}^2(\mbox{\boldmath$\varrho$})>- <{\bf
q}(\mbox{\boldmath$\varrho$})>^2 \propto
1/\mbox{\boldmath$\varrho$}^2$, so that $\varrho \leq \sigma$.

Let us consider now the general case $\Sigma_z \neq \Sigma_y$ for enough large displacement of 