TITLE:
Quantum Theory of the Wannier Phenomenon
AUTHORS:
Hubert Klar
KEYWORDS:
Born-Oppenheimer, Wannier Theory, Non-Separable Wave Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.11,
November
16,
2020
ABSTRACT: We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation [1] to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e-+ He(1s ns)→He-**for n ≫ 1. Along these lines we replace the standard BO set of potentials by an evolution operator. In this way we take a momentum-momentum coupling inadvertently disregarded by BO into account. The BO eigenvalue problem is now replaced by an evolution equation. One eigen-evolution has been identified as Wanner channel. That channel describes the diffraction of electron pairs from a potential ridge. That diffraction causes a phase jump of π/2 in the channel evolution. Moreover we present a new conservative attractive force controlling the motion of the electron pair as a whole in the nuclear field whose potential is given by . The coupling constant g has been calculated. That potential foreign to the standard BO approximation manifests itself by an entirely new series of isolated resonances located slightly below the double ionization threshold. This resonance ensemble compares favorably with experimental data. Further we present an evolution which forces the electron pair to the electrostatically unstable top of the potential ridge. That evolution may be regarded as quantum version of Wannier’s converging trajectory, and manifests itself here as Fresnel distribution.