Dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering inc luding the effects of nuclear dynamics by extending the common many-body Gr een's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and th e nuclear motion of the target molecule on the same footing whereby the dyn amical optical potential rigorously accounts for the complex many-body natu re of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximati on to the dynamical optical potential even when projectile and nuclear moti on are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the in influences of the nuclear dy namics on the optical potential to become relevant. For these cases, a syst ematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields nonlocal operators with respect to the n uclear coordinates. [S1050-2947(99)02210-6].