TITLE:
Insight into Electronic Transitions
AUTHORS:
Hubert Klar
KEYWORDS:
Many-Body Coulomb dynamics, Nonseparable Systems, Correlation, Wannier Phenomenon
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.10,
October
30,
2024
ABSTRACT: We present a scattering theory for charged particles suitable for electron atom collisions. Starting from the Hamilton-Jacobi equation for N electrons in the field of a nucleus or an ion core, we derive a parabolic differential equation that resembles the heat equation. We identify a Fresnel distribution as the main ingredient of its kernel. In particular, we show that high multiply excited states are strongly suppressed increasingly so for approaching the ionization threshold. That effect compares favorably with experimental data. Also, the Wannier channel is controlled by a Fresnel distribution. Moreover, that channel represents a novel continuum to our knowledge that has never been considered so far. The classical action has been employed to derive quatum wave functions in the semiclassical limit. The curvature of the N-elctron potential surface is shown to be the essential ingredient of an initial value problem for elastic and/or inelastic processes. The spectral region near the ionization threshold needs a special action to describe the Wannier phenomenon. This Wannier channel manifests itself by a novel continuum never considered before.