Theory of resonance and threshold effects in electron-molecule collisions: The projection-operator approach

A review is given of the development of the projection-operator formalism of Feshbach towards a comprehensive theory of resonance and threshold effects in electron-molecule collisions. The definition and explicit construction of the appropriate projectors is discussed. The threshold behavior of the singularities of the analytically continued fixed-nuclei electron-molecule scattering matrix is analyzed in order to characterize threshold effects in vibrational excitation by electron impact and dissociative electron attachment. The theory of the dynamics of electron-molecule collision complexes (vibration, dissociation, and autodetachment) is developed, using the methods of time-independent scattering theory as well as a time-dependent wave-packet description. The present stage of development of the theory is illustrated by the review of a few representative applications.