determines orientation of radius-vector $\mathbf{r}$ from the center of the frame system to point where wave function of photon describes its “appearance”. Using such a logic, we have: $$\mathbf{n}_{ph} = \mathbf{n}^{i}_{r} = \mathbf{n}^{f}_{r} = \mathbf{n}_{r}.
\label{eq.2.5.1}$$ As we use the frame system where axis $z$ is parallel to vector $\mathbf{k}$ of the photon emission, then dependent on $\mathbf{r}$ integrant function in the matrix element represents amplitude (its square is probability) of appearance of the particle at point $\mathbf{r}$ after emission of photon, if this photon has emitted along axis $z$. Then angle $\theta$ (of vector $\mathbf{n}_{\mathbf{r}}$) is the angle between direction of the particle motion (with possible tunneling) and direction of the photon emission.

Let us consider the angular integral in (\[eq.2.4.12\]) over $d\,\Omega$. Using (\[eq.2.5.1\]), we find: $$\begin{array}{l}
  \displaystyle\int \:
    Y_{lm}^{*}({\mathbf n}_{r}) \,
    Y_{1,-\mu^{\prime}}(\mathbf{n}_{r}) \,
    Y_{n, \mu-\mu^{\prime}}^{*}(\mathbf{n_{r}}) \;
    d\Omega = \\

  = (-1)^{l+n-\mu^{\prime}+1 + \frac{|m+\mu^{\prime}|}{2}} \; i^{l+n+1} \;
    \sqrt{\displaystyle\frac{3\,(2l+1)\,(2n+1)}{32\pi}\;
          \displaystyle\frac{(l-1)!}{(l+1)!} \;
          \displaystyle\frac{(n-|m+\mu^{\prime}|)!}{(n+|m+\mu^{\prime}|)!}} \;
    \times \\
  \;\times
    \displaystyle\int\:
      P_{l}^{1}(\cos{\theta}) \; P_{1}^{1}(\cos{\theta}) \; P_{n}^{|m+\mu^{\prime}|} (\cos{\theta}) \cdot
      \sin{\theta} \, d\theta \,d\varphi,
\end{array}
\label{eq.2.5.2}$$ where $P_{l}^{m}(\cos{\theta})$ are *associated Legandre’s polynomial* (see [@Landau.v3.1989], p. 752–754, (c,1)–(c,4); also see [@Eisenberg.1973] (2.6), p. 34) and the following restrictions on possible values of $m$ and $l_{f}$ have 