A purely classical description of crossings of energy levels and spectroscopic signatures of charge exchange

Abstract

Charge exchange and crossings of corresponding energy levels that enhance charge exchange are strongly connected with problems of energy loss and diagnostics in high-temperature plasmas. Charge exchange has also been proposed as one of the most effective mechanisms for population inversion in the soft x-ray and VUV ranges. One area of the most fundamental theoretical importance in the study of charge exchange is the problem of electron terms in the field of two stationary Coulomb centres (TCC) of charges Z and Z' separated by a distance R. This involves fascinating atomic physics: the terms can have crossings and quasicrossings. These rich features of the TCC problem are also manifest in other areas of physics such as plasma spectroscopy: a quasicrossing of the TCC terms, by enhancing charge exchange, can result in an unusual structure (a dip) in the spectral line profile emitted by a Z-ion from a plasma consisting of both Z- and Z'-ions, as has been shown theoretically and experimentally. The paradigm is that these sophisticated features of the TCC problem and their flourishing applications are inherently quantum phenomena. In this paper we disprove this paradigm. We present a purely classical description of both the crossings of energy levels in the TCC problem and the dips in the corresponding spectral line profiles caused by the crossing (via enhanced charge exchange). Our classical description is based on first principles and does not use any model assumptions.

Electric field induced crossings of energy terms of a Rydberg quasi molecule enhancing charge exchange and ionization

“…It has a V-type crossing with term 3, which asymptotically is the Z′-term (Z min = Z′ for Z′ < Z). At r → ∞, term 1 corresponds to the energy of a hydrogen-like ion of the nuclear charge Z max slightly perturbed by the charge Z min [18,19]. As for term 2, at r → ∞ it has properties similar to term 4, but with the interchange of Z max and Z min .…”

“…If the ratio Z′/Z is of the order of (but not equal to) unity, this term at r → ∞ can be described only in the terminology of elliptical coordinates (rather than parabolic or spherical coordinates), meaning that even at r → ∞ the electron is shared between the Z-and Z′-centers. However, in the case of Z′ ≫ Z, this term can be asymptotically considered as the Z′-term [18,19]. It has the V-type crossing with term 3, which asymptotically is the Z-term (Z min = Z for Z′ > Z).…”

“…It has the V-type crossing with term 3, which asymptotically is the Z-term (Z min = Z for Z′ > Z). Likewise, in the case of Z′ ≪ Z, term 4 can be asymptotically considered the Z-term [18,19]. It has a V-type crossing with term 3, which asymptotically is the Z′-term (Z min = Z′ for Z′ < Z).…”

“…But then in 2000 one of the authors published papers [18,19] presenting a purely classical description of both the crossings of energy levels in the TCC problem and the dips in the corresponding spectral line profiles caused by the crossing (via enhanced charge exchange). These classical results were obtained analytically based on first principles without using any model assumptions.…”

Conic-Helical Motion in the Three-Body Problem: Star-Planet-Moon Systems and Relativistic Effects in Binary-Star-Planet Systems

“…Conic-helical orbits in 3D3BS-the astrophysical analogue of 1-electron Rydberg quasi molecules studied previously by Oks [1,2] are of interest for several reasons. First, the possibility of stable (or metastable) conic-helical orbits in 3D3BS is a fundamental problem in its own right, as a relatively new chapter of the centuries-old classical three-body problem.…”