  The dynamics of entanglement during the low energy scattering processes in
bipartite systems at the presence of a laser field is studied, using the
Kramers-Henneberger unitary transformation as the semi classical counterpart of
the Block-Nordsieck transformation, in the quantizied field formalism. The
Stationary-state Schrodinger equation for quantum scattering process is
obtained for such systems. Then, by using partial wave analysis, we introduce
new form of entanglement fidelity containing high intense laser field.
Therefore, the effective potential of hot quantum plasmas including plasmon and
quantum screening effect is used to show entanglement fidelity ratio as a
function of the laser amplitude, plasmon parameter and the Debye length
parameter for elastic electron-ion collisions. It is shown that the amplitude
of laser beam or free electron oscillation play important roles in the
evolution of entanglement of the system.
