reflection above the barrier. In such cases the two effects do not cancel and the Langevin theory underestimates the reaction probability.

Analyzing Fig. \[Ferm\] one can develop relatively a simple approximation, allowing one to calculate the integral in Eq. . It is based on the observation that the reaction probability $P$ is almost symmetric with respect to the point where $P = \frac12 P^{\mathrm}{re}$, similarly to the Fermi distribution. The integral corresponding to the area below the distribution can be calculated by approximating it by a rectangle $$K^{\mathrm}{re} \approx g \frac{\pi \hbar}{\mu k} P^{\mathrm}{re} \ell^\ast (\ell^\ast +1),$$ where $\ell^\ast$ is the angular momentum corresponding to the point where $P = \frac12 P^{\mathrm}{re}$ $$\label{P12}
P = \frac{P^{\mathrm}{re}}{P^{\mathrm}{re} e^{ 2 \pi \varepsilon(\ell^\ast,E)} + 1} = \frac {P^{\mathrm}{re}}{2}.$$ In the universal case $y=1$ the above equation yields $\varepsilon = 0$, and in this particular case we recover the classical approximation.

In order to verify whether the contribution of quantum corrections due to shape resonances and quantum reflection is still important at high energies, Fig. \[myfigure\] depicts the quantum corrections for energies up to $10^6$ $E_n$ for two physically most important power law potentials. We also study the dependence of the quantum corrections on 