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Ionization of K-shell or, more generally, of deep inner-shell electrons in atoms and molecules is accompanied by a considerable rearrangement of the valence (outer-shell) electrons in response to the reduced shielding of the nuclear attraction.(1) This adjustment of the valence electrons, referred to as electronic relaxation, leads to a significant energy lowering of the final ionic state relative to a state where the valence electron distribution of the initial state is maintained (“frozen”). The magnitude of this relaxation energy scales with the number of valence electrons.(2,3) In the case of the K-shell ionization of second-row atoms (Z = 3−10), for example, the relaxation energies (in eV) are approximately given by E R(Z) = 3.1 (Z − 2.2). In a molecular environment the corresponding relaxation energies are typically 2−3 eV larger than the values for the free atom. Relaxation not only plays a role in the ionic core but also affects the motion of the outgoing photoelectron. The relaxation of the valence electrons, being essentially a contraction of the valence charge distribution, quite effectively screens the inner-shell hole potential experienced by the photoelectron. This means that the potential of the relaxed ionic core is less attractive than its unrelaxed (frozen) counterpart. As a consequence, resonances in the photoionization cross section will appear at higher energy for a relaxed core than for an unrelaxed (frozen) core. Concomitantly with the shift to higher energy, the resonance peaks will be lowered and broadened as a result of relaxation.

Recent advances in tunable laser sources have stimulated a great deal of interest in the study of intense field-matter interaction physics. Whenever a molecule interacts with an intense radiation field, it can absorb multiple photons from the field and make a transition either to an excited state (excitation) or into the continuum (ionization). If the energy of an integral number of photons equals the energy difference between the initial and an excited state, the multiphoton process becomes resonant and its probability is greatly enhanced. The observation of such resonant enhanced processes requires considerably less intensity than that required for non-resonant processes. Several researchers have taken advantage of this resonance enhancement to study various aspects of resonant enhanced multiphoton ionization (REMPI) processes in molecules.1 Measurement of ionic and photoelectron spectra have illustrated features such as non-Franck-Condon effects in ionic vibrational branching ratios due to autoionization,2 shape resonances3 and Cooper minima,4 non-atomic effects in ionization of Rydberg states5 and competition between rotational and vibrational autoionization.6

In this contribution we want to discuss several features and applications of the Schwinger variational principle to the study of collisions of low energy electrons with molecules and molecular ions. The Schwinger variational principle has long been known to be a potentially useful formulation of the collision problem but until recently there have been very few applications of this variational principle to electron collision problems.1