photon we have $$T_{ij}=\frac{l_f}{2\varepsilon\varepsilon'}\left(v \delta_{ij}-
 \frac{8}{\zeta^2}u_i u_j\right),\quad v=\frac{\varepsilon}{\varepsilon'}
 +\frac{\varepsilon'}{\varepsilon},\quad \zeta = 1+\gamma^2 \vartheta^2.
\label{3.9}$$

Finally, averaging the last expression over the azimuth angle of emitted photon we obtain $$T_{ij}=\frac{l_f}{2\varepsilon\varepsilon'}U(\zeta)
 \delta_{ij},\quad
U(\zeta)=v-\frac{4(\zeta-1)}{\zeta^2}.
\label{3.10}$$

Substituting the expression obtained into (\[3.7\]) we find the correction to the probability of photon emission connected with the restricted transverse dimensions of colliding beams of charged particles: $$dw_1=\frac{\alpha^3}{\pi
m^2}\frac{\varepsilon'}{\varepsilon}\frac{d
\omega}{\omega}U(\zeta) F(\omega, \zeta) d\zeta,
\label{3.11}$$ where $$\begin{aligned}
&& F(\omega, \zeta)=F^{(1)}(\omega, \zeta)-F^{(2)}(\omega,
\zeta),
\nonumber \\
&& F^{(1)}(\omega, \zeta)=\frac{2\eta^2}{\zeta^2}\int K_1^2(\eta
\varrho)\left(w_r({\bf x}+\mbox{\boldmath$\varrho$})-w_r({\bf
x})\right)w_c({\bf x})d^2xd^2\varrho,
\nonumber \\
&& F^{(2)}(\omega, \zeta)=\frac{2\eta^2}{\zeta^2}\int\left(\int
K_1(\eta \varrho)\frac{\mbox{\boldmath$\varrho$}}{\varrho}w_c({\bf
x}-\mbox{\boldmath$\varrho$})d^2\varrho \right)^2w_r({\bf x})d^2x,
\label{3.12}\end{aligned}$$ here $\eta=q_{min}\zeta$.

Using the integral $$\int K_1^2(\eta \varrho) \varrho d\varrho =
\frac{\varrho^2}{2}\left[K_1^2(\eta \varrho)-K_0(\eta
\varrho)K_2(\eta \varrho)\right]
\label{3.13}$$ and integrating by parts we obtain $$\begin{aligned}
&& F(\omega, \zeta)= \frac{\eta^2}{\zeta^2}\Big[\int
\left[K_0(\eta \varrho)K_2(\eta \varrho)-K_1^2(\eta
\varrho)\right]\varrho
\frac{d\Phi(\mbox{\boldmath$\varrho$})}{d\varrho}d^2\varrho
\nonumber \\
&& -2\int\left(\int K_1(\eta
\varrho)\frac{\mbox{\boldmath$\varrho$}}{\varrho}w_c({\bf
x}-\mbox{\boldmath$\varrho$})d^2\varrho \right)^2w_r({\bf
x})d^2x\Big],
\label{3.14}\end{aligned}$$ where $$\Phi(\mbox{\boldmath$\varrho$})=\int w_r({\bf
x}+\mbox{\boldmath$\varrho$}) w_c({\bf x})d^2x.
\label{3.15}$$

In the general case the axes of colliding beams are displaced with respect each other in the transverse plane by the vector ${\bf x}_0$ with coordinates $z_0,y_0$. In this case we have to consider $$w_r({\bf x}) \rightarrow w_r({\bf x}+{\bf
x}_0),~F^{(1,2)}(\omega, \zeta) \rightarrow F^{(1,2)}(\omega,
\zeta, {\bf x}_0),~ \Phi(\mbox{\boldmath$\varrho$}) \rightarrow
\Phi(\mbox{\boldmath$\varrho$}+{\bf x}_0)
\label{3.15a}$$

The first term in the 