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We derive a rigorous optical potential for electron-molecule scatteringincluding the effects of nuclear dynamics by extending the common many-bodyGreen's function approach to optical potentials beyond the fixed-nuclei limitfor molecular targets. Our formalism treats the projectile electron and thenuclear motion of the target molecule on the same footing whereby the dynamicaloptical potential rigorously accounts for the complex many-body nature of thescattering target. One central result of the present work is that the commonfixed-nuclei optical potential is a valid adiabatic approximation to thedynamical optical potential even when projectile and nuclear motion are(nonadiabatically) coupled as long as the scattering energy is well below theelectronic excitation thresholds of the target. For extremely low projectilevelocities, however, when the cross sections are most sensitive to thescattering potential, we expect the influences of the nuclear dynamics on theoptical potential to become relevant. For these cases, a systematic way toimprove the adiabatic approximation to the dynamical optical potential ispresented that yields non-local operators with respect to the nuclearcoordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.

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