TITLE:
Theory of Electronic Transitions
AUTHORS:
Hubert Klar
KEYWORDS:
Correlation, Electron Atom Scattering, Electron Pair Formation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
18,
2025
ABSTRACT: We investigate scattering of electrons from atoms in the nonrelativistic energy range. In contrast to the pioneer work by Born, we take correlation properly into account and describe electrons by waves rather than by mass points. To this end, we start from a novel parabolic partial differential equation, which resembles the inhomogeneous heat equation. Calculation of the kernels for incoming and outgoing waves allows us to formulate initial value problems. A converging Fresnel distribution is shown to control the incident electron and pulls the target electron onto an equilibrium location. The electron-electron interaction is here attractive. Finally, the two electrons are attracted by the nucleus and arrive at a triple condensation point, where they form a compound state comparable to a Cooper pair. This three-body configuration is highly unstable, described by an unstable Fresnel distribution, and leads finally to excited target states plus an escaping electron. There is no way for a one-step transition. The excitation process always goes through a ladder consisting of Fresnel states. The Wannier mode has been identified as an unstable Fresnel distribution, which is not an energy eigenstate, but it is an eigenstate of the action curvature. This unusual mode cannot be expected as a discrete line in a Rydberg spectrum, but seems to manifest itself as noise. We show that this noise is heavily suppressed near the threshold.