There are many areas of physics whose advance is dependent on the availability of data on collision processes between elec trons, ions, and neutral atoms and mole cules. In recent years this has been most apparent in astrophysics, atmospheric physics, laboratory plasmas (most notably in connection with the controlled ther monuclear fusion programmes), and gas lasers. In addition, the subject of atomic and molecular collisions is of great intrinsic interest, having played a leading role in the establishment of quantum theory, and in cludes many aspects of fundamental im portance in the understanding of atomic and molecular structure. One of the most powerful investigative tools at the disposal of the atomic and molecular physicist is the electron beam. Electrons are in many respects more ver satile than their nearest "competitor", the photon, being able to induce not only all the atomic and molecular transitions possi ble with photons, but also those normally forbidden to photons (e.g. s-s transitions). Indeed, electron beam technology today is such that the currents and resolutions now attainable make it competitive with the best available synchrotron radiation sources. And because high energy beams can be produced at a fraction of the cost, it has been aptly dubbed by many atomic physi cists as the "poor man's synchrotron". At low energies too, i.e. below the first ionisation threshold of the target, an elec tron beam can reveal a wealth of informa tion on the structure and properties of atoms and molecules. Especially in the last six to eight years, experimentalists have been able to produce, with improved tech niques, a plethora of cross sectional data for low energy electron scattering from atoms and molecules, providing an accu racy and detail which are a challenge to the theorist. In many cases, the most in teresting features which appear in their results, are the scattering resonances caus ed by the temporary formation of com pound states of the incident electron and the atomic or molecular target. These resonances are particularly significant in electron-molecule collisions, as they fre quently facilitate the transfer of energy from the electronic to the nuclear motion, leading to enhanced rotational and vibra tional excitation cross sections and, sometimes, even to molecular dissociation. Even in the non-resonant energy region, the determination of scattering cross sec tions is of interest and importance, for ex ample as necessary data for the interpreta tion of many astrophysical and atmo spheric processes. Whereas the challenge presented by low energy electron-atom investigations has been, and is being, met by theorists, the situation in electron-molecule scattering has been, until recently, more an embar rassment. To be fair, the development of a rigorous and feasible theory of low energy electron-molecule scattering is a non-trivial matter, and neither the techniques nor the computers able to solve the electronmolecule equations were available. How ever, the incentive injected into this subject by the experimentalists' success, coupled to the increased demand for electronmolecule cross sections from other areas of science, and not least, the marked im provement in computational facilities in re cent years, have encouraged theorists to look afresh at electron-molecule processes and to come up with some novel and very promising new approaches.
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