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.