Abstract
The wave equation for two electrons in an external Coulomb field (helium-like atoms) has been shown to be a problem in a three-dimensional half-space. The wave-equation becomes quasi-separable in inertial coordinates. This allows to work out the electron motion in the frame of principal inertia axes. We find that non-adiabatic coupling terms constitute a fictitious force and lead to a deformation of the static potential surface. Incoming and outgoing modes of electron pairs are studied in detail, and applied to the threshold ionization of hydrogen-like atoms by electrons. Our analysis confirms the classical work by Wannier. However, we go beyond Wannier and present bending and stretch vibrations of electron pairs. The bending vibration has no influence onto the total ionization cross-section. The pair formation below threshold destroys the existence of high double Rydberg resonances. Finally, we describe the propagation of an electron pair through a linear chain of Rydberg atoms.
Highlights
The motion of single electrons in atomic matter is basically well understood
We find that non-adiabatic coupling terms constitute a fictitious force and lead to a deformation of the static potential surface
Incoming and outgoing modes of electron pairs are studied in detail, and applied to the threshold ionization of hydrogen-like atoms by electrons
Summary
The motion of single electrons in atomic matter is basically well understood. our knowledge of the dynamics of few-electron complexes in external fields is still incomplete. For the ionization of a neutral atom by slow electron impact, a simple phase space consideration suggests a threshold cross-section being linear in the excess energy, i.e. σion ∝ E1. This is, in conflict with many experimental data. Wannier has successfully described the motion of an electron pair in an external Coulomb field. It is far from trivial how (2) derives from quantum mechanics see e.g. We re-derive (2) for ionization and present an alternative electron-electron attraction mechanism for electron pairs in an external Coulomb field.
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