Models of inner-shell vacancy production which include translation factors are developed for the change transfer process in ion-atom collisions. Translation factors are included in the basis set in which the electronic wavefunction is expanded in order to correctly describe the motion of the electron during the collision. Though several numerical studies have been done which employ this concept, the present models for change exchange are based on stationary state expansions. We first formulate the problem in the adiabatic framework. Having chosen a case in which the form of the translation factors is simple and in which additional approximations may be made, i.e., the case of long-range coupling, all terms in the equations of motion can be evaluated in closed form. An analytic solution is derived with the adiabatic theory which shows explicitly the effect of translation factors on the sharing ratio (defined as the ratio of vacancy production cross-sections of the high Z to low Z partners). The result reduces to that of the Demkov model in the low velocity limit. As the velocity increases, we predict a sharing ratio which drops below the Demkov curve and reaches a maximum at finite velocity. Numerical calculations using translation factors in a molecular orbital basis exhibit such a fall-off. We show that this effect is due solely to the inclusion of the momentum transfer of the electron. The assumptions of the adiabatic approach, however, limit its application to the low velocity region. We develop a new formulation of the problem which is not limited by the adiabatic assumptions. We obtain solutions of the equations of motion in closed form. This new treatment gives not only the correct adiabatic limit but also the exact Born result directly from the analytic solution of the coupled equations. Thus, translation factors are shown to provide a unification between an adiabatic Demkov-type approach and first-order perturbation theory at high velocity with a formalism which retains unitarity. In addition, it offers new insights onto the competing effects taking place in the collision process as a function of velocity and, within the approximations made, describes the intermediate velocity region which cannot be treated by either the adiabatic or high velocity, perturbation theories.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/281899 |
| Date | January 1980 |
| Creators | Pfeifer, Shirley Jane |
| Contributors | Garcia, J. D. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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