Differential cross section for molecular ionization by electron impact in the adiabatic approximation.

Abstract

Molecular ionization by electron impact is examined in the Born-Oppenheimer approximation where the rotational and vibrational motions of the nuclei are considered separable. Expressions for the differential cross section, applicable to an exact treatment of the adiabatic electronic wave functions, are derived in terms of a momentum-transferred summation for three levels of experimental resolution, spatially unpolarized, spatially unpolarized and rotationally unresolved, and spatially unpolarized and rotationally and vibrationally unresolved. Several possible advantages of a momentum-transferred summation relative to a partial-wave summation are discussed. Most importantly, the expected relatively rapid convergence of the momentum-transferred summation effectively reduces the number of transition matrix elements which must be calculated. Additionally, the momentum-transferred summation involves an ''incoherent'' summation which, in general, is more easily computed. Lastly, we present explicit expressions for the transition probabilities in the plane-wave and distorted-wave Born approximations.