  We study the effect of screening by bound electrons in low energy nuclear
reactions. We use molecular dynamics to simulate the reactions involving many
electrons: D+$d$, D+D, $^3$He+$d$, $^3$He+D, $^6$Li+$d$, $^6$Li+D, $^7$Li+$p$,
$^7$Li+H. Quantum effects corresponding to the Pauli and Heisenberg principles
are enforced by constraints in terms of the phase space occupancy. In addition
to the well known adiabatic and sudden limits, we propose a new "dissipative
limit" which is expected to be important not only at high energies but in the
extremely low energy region. The dissipative limit is associated with the
chaotic behavior of the electronic motion. It affects also the magnitude of the
enhancement factor. We discuss also numerical experiments using polarized
targets. The derived enhancement factors in our simulation are in agreement
with those extracted within the $R$-matrix approach.
