A Unified View of Collisions and Spectra
The interaction of electrons in an atomic system has historically and traditionally been viewed as falling into two main categories, spectroscopy and collisions. Pedagogically as well, most textbooks in quantum mechanics make this division, devoting their initial discussion to bound state problems and turning in later chapters to scattering. This dichotomy is artificial. Over the past two decades, research in atomic physics has in fact shown the usefulness, even as a point of view, of giving up the division into two categories and seeing both kinds of processes as essentially related. Thereby, links are established between elastic and inelastic electron atom scattering on the one hand and processes involving radiation such as photo absorption and ionization on the other.
These links are specifically codified in what has come to be called Quantum Defect Theory. The effects of interactions at short range are separated from those arising at larger values of the radial distance r of an electron from the rest of the atom. The latter is usually motion in a standard field such as the Coulomb field and can be handled analytically. It is also this latter motion which alone is sensitive to the asymptotic kinetic energy of the electron, so that discrete and continuum states are distinguished only in this large-r behavior. The short range behavior involves multi-particle aspects of the problem, nonlocal (exchange) forces and other such complications but, on the other hand, is insensitive to energy so that it can be parameterized by a limited set of quantities common to both bound and scattering states. Also, since this part of the study is restricted to a finite volume, the numerical calculations can be kept to a modest size.
This set of lectures will be an introduction to the unified view of collisions and spectroscopy. Starting with a simple illustration in potential scattering, we will move on to electron-atom scattering in both single and many channel contexts. Key elements to be presented are quantum defect theory and the basic parameters of that theory, and the so-called method of frame transformations for linking alternative descriptions that are suitable for describing the small- and large-r behavior. Negative ions and neutral atoms with closed shells are used for illustrative purposes.
KeywordsOutgoing Wave Coulomb Field Bound State Energy Fragmentation Channel Ionization Limit
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