Projection and Quasi-Projection Operators for Electron Impact Resonances on Many-Electron Atomic Targets
In Chapter 1, we dealt with the theory and applications of the projection-operator formalism to two-electron systems. The reason for singling out two-electron autoionization systems (implying a one-electron target) was given in Chapter 1; to repeat briefly, the fact that the target eigenfunctions are known analytically and the special character of a one-electron target allow exact projection operators in the Feshbach sense(1) to be written down, which thereby allows precision calculations of the composite (two-electron) system approaching the accuracy of ordinary two-electron bound-state systems to be carried out [cf., for example, Ref. 2]. In the case of autoionization of two- or more electron target systems, the inability of achieving comparable precision arises from two causes: not only can we not give the exact eigenfunctions analytically, but we cannot even supply a formal, explicit expression for the projection operators that we need at the outset.
KeywordsProjection Operator Radial Function Shape Resonance Feshbach Resonance Electron Target
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- 28.A. Temkin and A. K. Bhatia, in Electron Scattering front Atoms and Atomic Ions, a satellite symposium of the 1981 ICPEAC, Program-Abstract Booklet, unpublished.Google Scholar