  Using a semiclassical mean field theory, we show that the screening potential
exhibits a characteristic radial variation in the tunneling region in sharp
contrast to the assumption of the constant shift in all previous works. Also,
we show that the explicit treatment of the tunneling region gives a larger
screening energy than that in the conventional approach, which studies the time
evolution only in the classical region and estimates the screening energy from
the screening potential at the external classical turning point. This
modification becomes important if the electronic state is not a single
adiabatic state at the external turning point either by pre-tunneling
transitions of the electronic state or by the symmetry of the system even if
there is no essential change with the electronic state in the tunneling region.
