and $d\nu_{f}$ are intervals defined for photon and particle in the final $f$-state, $d\Omega_{ph} = d\,\cos{\theta_{ph}} = \sin{\theta_{ph}} \,d\theta_{ph} \,d\varphi_{ph}$, $k_{ph}=w/c$. $F_{fi}$ is integral over space with possible summation by some quantum numbers of the system in the final $f$-state. Such procedure is averaging by these characteristics and $F_{fi}$ is independent on them. Then, interval $d\,\nu_{f}$ has only new characteristics and quantum numbers, by which integration and summation in $F_{fi}$ was not fulfilled. Integrating eq. (\[eq.2.8.1\]) over $dw$ and substituting eq. (\[eq.2.1.2\]) for $F_{fi}$, we find: $$\begin{array}{cc}
  d W = \displaystyle\frac{Z_{eff}^{2} \,e^{2}}{m^{2}}\:
        \displaystyle\frac{\hbar\, w_{fi}}{2\pi \,c^{3}} \; \Bigl|p(k_{i}, k_{f})\Bigr|^{2} \;
        d \Omega_{ph} \, d\nu_{f}, &
  w_{fi} = w_{i} - w_{f} = \displaystyle\frac{E_{i} - E_{f}}{\hbar}.
\end{array}
\label{eq.2.8.2}$$ This is the probability of the photon emission with impulse $\mathbf{k}$ (and with averaging by polarization $\mathbf{e}^{(\alpha)}$) where the integration over angles of the particle motion after the photon emission has already fulfilled. To take direction $\mathbf{n}_{\mathbf{r}}^{f}$ of motion (or tunneling) of the particle after emission into account, I define the probability so: *the concerning angle $\theta$ is such a function, definite integral of which by the angle $\theta$ with limits from 0 to $\pi$ corresponds exactly to the total probability of photon emission (\[eq.2.8.2\])*: 