Tunneling of slow quantum packets through the high Coulomb barrier

We study the tunneling of slow quantum packets through a high Coulomb barrier. We show that the transmission coefficient can be quite different from the standard expression obtained in the plane wave (WKB) approximation (and larger by many orders of magnitude), even if the momentum dispersion is much smaller than the mean value of the momentum. •Tunneling of quantum packets through high Coulomb barrier.•Transmission probability is much higher than for plain waves.•Transmission probability strongly depends on the packet shape.•Transmission probability can depend on the momentum variance only.•The concept of effective Planck constant does not work.