  We calculate the electron screening effect in low energy nuclear fusion
reactions by taking non-adiabaticity of the tunnleing process into account. In
order to investigate deviations from the adiabatic limit, we use the dynamical
norm method, which has recently been developed by the present authors. Using
$d$+D reaction as an example, we show that the screening energy never exceeds
those estimated in the adiabatic approximation. Our calculations indicate that
the non-adiabatic effect is important both in classically allowed and
classically forbidden processes.
