  The problem of wave packet tunneling from a parabolic potential well through
a barrier represented by a power potential is considered in the case when the
barrier height is much greater than the oscillator ground state energy, and the
difference between the average energy of the packet and the nearest oscillator
eigenvalue is sufficiently small. The universal Poisson distribution of the
partial tunneling rates from the oscillator energy levels is discovered. The
explicit expressions for the tunneling rates of different types of packets
(coherent, squeezed, even/odd, thermal, etc.) are given in terms of the
exponential and modified Bessel functions. The tunneling rates turn out very
sensitive to the energy distributions in the packets, and they may exceed
significantly the tunneling rate from the energy state with the same average
number of quanta.
