has been constructed. Inside region of the $\alpha$-active nuclei from $^{106}{\rm Te}$ up to the nucleus with numbers of nucleons and protons $A_{p}=266$ and $Z_{p}=109$ with energy of the photons emitted from 50 keV up to 900 keV good agreement has been achieved between the spectra, obtained on the basis of the multipole model, and the bremsstrahlung spectra obtained on the basis of the proposed formula. At finishing, results are summarized.

Model \[sec.2\]
===============

Matrix element of emission \[sec.2.1\]
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We define probability of the bremsstrahlung emission during $\alpha$-decay of nucleus in terms of transition matrix element of the composite system ($\alpha$-particle and daughter nucleus) from its state before emission of photon (called as *initial $i$-state*) into its state after such emission (called as *final $f$-state*). In this paper, I shall use the definition of the matrix element like (2.11) in [@Maydanyuk.2003.PTP] (in the first correction of the non-stationary perturbation theory with stationary limits $t_{0}=-\infty$ and $t_{1}=+\infty$, and with normalization $|C| \to 1$): $$a_{fi} = F_{fi} \cdot 2\pi \,\delta(w_{f}-w_{i}+w),
\label{eq.2.1.1}$$ where $$\begin{array}{lcl}
  F_{fi} & = &
    Z_{eff}\, \displaystyle\frac{e}{m} \,
    \sqrt{\displaystyle\frac{2\pi\hbar}{w}} \cdot p\,(k_{i},k_{f}), \\

  p\,(k_{i}, k_{f}) & = &
    \displaystyle\sum\limits_{\alpha=1,2} \mathbf{e}^{(\alpha),*}\, \mathbf{p}\,(k_{i}, k_{f}), \\

  \mathbf{p}\,(k_{i}, k_{f}) & = &
    \biggl< k_{f} 