dimensionless units defined by $R_n$ and $E_n$.

Applying Eq.  with the energy $$\begin{split}
\varepsilon(\ell,E) = &(n/2)^{(2/(n-2))} \frac{1}{\sqrt{2n-4}} E (l(l+1))^{-\frac{n+2}{2n-4}}\\
&- \sqrt{\frac{n}{2}-1}  \frac{\sqrt{l(l+1)}}{n}
\end{split}$$ obtained by fitting the parabolic potential to the centrifugal barrier for $V(r)=-1/r^n$, and integrating over angular momenta $\ell$ we get $$\begin{split}
\label{Kre6}
\mathcal{K}^{\mathrm}{re} \stackrel{E\to\infty}{\longrightarrow}  &g \frac{h}{2 \mu k} \int_0^{\infty} d \ell (2\ell+1) P(\ell,y)\\
 &= g \frac{h}{2 \mu k} \int_0^{\infty} d \ell (2\ell+1) \frac{P^{\mathrm}{re}}{P^{\mathrm}{re} e^{\varepsilon(\ell,E)}+1}
\end{split}$$ The reaction probability $P(\ell,y)$ as a function of the continuous variable $\ell(\ell+1)$ is shown in Fig. \[Ferm\]. The figure compares the reaction probability calculated from the parabolic potential approximation with the classical approach assuming that only collisions with energies above the barrier contribute to the reaction rate. The latter exhibits a step-like behavior, while the former is reminiscent of a Fermi distribution. The classical description does not include the contribution from the shape resonances, and at the same time overestimates the reaction rate in the regime affected by the quantum reflection. In the universal regime $y=1$ both contributions are almost equal, and in this particular case the Langevin approximation works relatively well. In contrast, for $y<1$ the contribution from the shape resonances is typically larger than the modification due to the quantum 