By K. Blum, H. Kleinpoppen (auth.), Juergen Hinze (eds.)

The papers gathered during this quantity were awarded in the course of a workshop on "Electron-Atom and Molecule Collisions" held on the Centre for Interdisciplinary stories of the college of Bielefeld in might 1980. This workshop, a part of a bigger application excited by the "Properties and Reactions of remoted Molecules and Atoms," thinking about the speculation and computational ideas for the quanti­ tative description of electron scattering phenomena. With the advances that have been made within the actual quantum mechanical characterisation of certain states of atoms and molecules, the extra advanced description of the unbound platforms and resonances vital in electron collision methods has matured too. As expli­ cated intimately within the articles of this quantity, the speculation for the quantitative clarification of elastic and inelastic electron molecule collisions, of picture- and a number of photon ionization or even for electron impression ionization is definitely constructed in a sort which lends itself to a whole quantitative ab initio interpretation and pre­ diction of the observable results. a few of the studies received and the innovations that have developed through the years within the com­ putational characterization of sure states became a necessary foundation for this improvement. to make sure, a lot has to be performed prior to we've a whole and specific theoretical figuring out of the recognized collisional approaches and of the phenomena and results, that may nonetheless be un­ coated with the continued refinement of the experimental tech­ niques.

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The variational K-matrices, obtained using only a single s Gaussian basis function on each nucleus and shown in the n = 0 column of Table I, suggest that the Schwinger method may provide accurate solutions of the scattering problem with small discrete basis sets. 36 Table I. R. R. LUCCHESE ET AL. 5 au. 045 -1. 552 -1. (19). As a practical consideration the degree of convergence of the approximate wave function at any step of the procedure can be judged by how well these nonvariational approximations agree with each other and with the variationally stable estimates of Table I.

Rev. A ll,488(1980). SCHWINGER VARIATIONAL PRINCIPLE 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 49 R. K. Nesbet, J. Chern. Phys. 40, 3619 (1964). P. E. Cade, K. D. Sales, and A. C. Wahl, J. Chern. Phys. ~, 1973 (1966). R. R. Lucchese and V. McKoy, "An iterative approach to the Schwinger variational principle applied to electron-molecular ion collisions," Phys. Rev. A (1981) - in press. D. Robb and L. Collins, Phys. Rev. A 22, 2474 (1980). T. Kato, Phys. Rev.

These sources give an excellent summary of both mathematical and computational techniques in complex scaling through 1978. The scope of this talk will be limited to several developments since 1978 with which I have been connected. The first of these developments is a discussion of direct methods for computing partial resonance widths. lex resonance energy computed by any direct method gives only the total resonance width, but it can be shown that the eigenfunction associated with the complex resonance eigenvalue can be used to provide partial width information - a simple consequence of the separable nature of the S-matrix near a resonance.

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