analog in a general case in Appendix \[app.7\]): $$\begin{array}{lcl}
  \Bigl\langle f \Bigl|\, \displaystyle\frac{\partial}{\partial \mathbf{r}}\, \Bigl|\, i \Bigl\rangle =
  \displaystyle\frac{1}{w_{fi}}\;
    \biggl\langle f\,
    \biggl|\,
      \displaystyle\frac{\partial\, V(\mathbf{r})}{\partial \mathbf{r}}\,
    \biggr|\, i \biggr\rangle,
\end{array}
\label{eq.2.7.1.2}$$ we obtain: $$p\,(k_{i}, k_{f}) =
  \displaystyle\frac{1}{w_{fi}}
    \sum\limits_{\mu = -1, 1}  h_{\mu}\,\mathbf{\xi}^{*}_{\mu}
    \int
      \psi^{*}_{f}(\mathbf{r})\:\psi_{i}(\mathbf{r})\;
      \displaystyle\frac{\partial\, V(\mathbf{r})}{\partial \mathbf{r}}\; \mathbf{dr}.
\label{eq.2.7.1.3}$$ In the spherically symmetric approximation of the $\alpha$-decay we use the wave functions in form (\[eq.2.4.2\]) and then the matrix element transforms into $$p\,(k_{i}, k_{f}) =
  \displaystyle\frac{1}{w_{fi}}
    \sum\limits_{\mu = -1, 1}
    \sum\limits_{m_{f}}\:
      h_{\mu}\,\mathbf{\xi}^{*}_{\mu}
    \displaystyle\int\limits^{+\infty}_{0} r^{2} dr
    \displaystyle\int d\Omega \cdot
      \varphi_{f}^{*} (r) \: Y_{l_{f}m_{f}}^{*} ({\mathbf n}_{r}^{f}) \cdot
      \varphi_{i} (r) \cdot
      \displaystyle\frac{\partial\, V(r)}{\partial \mathbf{r}}.
\label{eq.2.7.1.4}$$ After use of the gradient formula (\[eq.2.4.7\]) at $l_{i}=0$ and taking into account form (\[eq.2.4.11\]) for the spherical function $\mathbf{T}_{01,0}(\mathbf{n}_{r})$, this matrix element is separated into radial and angular integrals: $$\begin{array}{ccl}
  p\,(k_{i}, k_{f}) & = &
  -\,\displaystyle\frac{1}{w_{fi}}\,
    \sqrt{\displaystyle\frac{1}{3}}
    \displaystyle\sum\limits_{\mu = -1, 1} h_{\mu}
    \displaystyle\sum\limits_{\mu^{\prime} = \pm 1}
      \mathbf{\xi}^{*}_{\mu}\,\mathbf{\xi}_{\mu^{\prime}}
      \displaystyle\int\limits^{+\infty}_{0}
        \varphi_{f}^{*}(r)\;
        \varphi_{i} (r)\: \displaystyle\frac{d\, V(r)}{dr}\;
        r^{2} dr\; \cdot
    \displaystyle\sum\limits_{m_{f}}\:
      \displaystyle\int
        Y_{l_{f}m_{f}}^{*} ({\mathbf n}_{r}^{f})\;
        Y_{1,-\mu^{\prime}}(\mathbf{n}_{r})\; d\Omega
\end{array}
\label{eq.2.7.1.5}$$ or ($\mathbf{\xi}_{\pm 1}$ and $\mathbf{\xi}_{\pm 1}^{*}$ are orthogonal vectors) $$\begin{array}{lcl}
  p\,(k_{i}, k_{f}) =
  -\,\displaystyle\frac{1}{w_{fi}}\,
    J_{\rm dip}\, (l_{f}) \cdot
    I_{\rm dip}\, (l_{f}),
\end{array}
\label{eq.2.7.1.6}$$ where $$\begin{array}{lcl}
  J_{\rm dip}\, (l_{f}) & = &
    \displaystyle\int\limits^{+\infty}_{0}
      \varphi_{f}^{*}(l_{f}, 