spectroscopy of ions one should mention the X-ray laser problem. It has stimulated
a great number of papers, devoted to modelling the elementary processes in laser,
collisionally pumped plasmas (see [3, 4] and Refs. therein) and construction of the
first VUV and X-ray lasers with using plasmas of Li-, Ne-like ions as an active
medium. Very useful data on the X-lasers problem are collected in the papers by
Ivanova et al. (see [3–6] and Refs. therein). From the other side, studying spectra of
ions in plasmas remains very actual in order to understand the plasmas processes
themselves. In most plasmas environments the properties are determined by the
electrons and the ions, and the interactions between them. The electron-ion collisions play a major role in the energy balance of plasmas. For this reason, modelers
and diagnosticians require absolute cross sections for these processes. The cross
sections for electron-impact excitation of ions are needed to interpret spectroscopic
measurements and for simulations of plasmas using collisional-radiative models. At
present time a considerable interest has been encapsulated to studying elementary
atomic processes in plasmas environments (for example, see [1–30] and Refs.
therein) because of the plasmas screening effect on the plasmas-embedded atomic
systems. In many papers the calculations of various atomic and ionic systems
embedded in the Debye plasmas have been performed [11, 12, 16, 29, 30]. Calculation of emission spectra of the plasmas ions based in the precise theoretical
techniques is practical tool, which may be used instead of very expensive sophisticated experiments. Nevertheless, there are known principal theoretical problems to
be solved in order to receive the correct description of master parameters of the
elementary atomic processes in laser, collisionally pumped plasmas. First of all,
speech is about development of the advanced quantum-mechanical models for the
further accurate computing oscillator strengths, electron-collisional strengths and
rate coefficients for atomic ions in plasmas, including the Debye plasmas. As
usually, a correct accounting of the relativistic, exchange-correlation, a plasmas
environment effects is of a great importance. To say strictly, solving of the whole
problem requires a development of the quantum-electrodynamical approach as the
most consistent one to problem of the Coulomb many-body system.
In this chapter we present the fundamentals of an advanced relativistic energy
approach, based on the Gell-Mann and Low formalism, to studying spectroscopic
characteristics of the multicharged ions in the Debye plasmas, in particular, computing the electron-ion collision strengths, cross-sections etc. The approach is
combined with relativistic many-body perturbation theory (PT) with the Debye
shielding model Hamiltonian for electron-nuclear and electron-electron systems.
The optimized one-electron representation in the PT zeroth approximation is constructed by means of the correct treating the gauge dependent multielectron contribution of the lowest PT corrections to the radiation widths of atomic levels. It is
worth to remind that the method of the relativistic many-body PT formalism is
constructed on the base of the same ideas as the well-known PT approach with the
model potential zeroth approximation by Ivanov-Ivanova et al. [31–44]. However
there are a few fundamental differences. For example, in our case the PT zeroth
approximation [51, 54] is in fact the Dirac- Debye-Hückel one. In order to calculate
the radiative and collisional parameters an effective gauge-invariant version of
56
A. V. Glushkov et al.
a great number of papers, devoted to modelling the elementary processes in laser,
collisionally pumped plasmas (see [3, 4] and Refs. therein) and construction of the
first VUV and X-ray lasers with using plasmas of Li-, Ne-like ions as an active
medium. Very useful data on the X-lasers problem are collected in the papers by
Ivanova et al. (see [3–6] and Refs. therein). From the other side, studying spectra of
ions in plasmas remains very actual in order to understand the plasmas processes
themselves. In most plasmas environments the properties are determined by the
electrons and the ions, and the interactions between them. The electron-ion collisions play a major role in the energy balance of plasmas. For this reason, modelers
and diagnosticians require absolute cross sections for these processes. The cross
sections for electron-impact excitation of ions are needed to interpret spectroscopic
measurements and for simulations of plasmas using collisional-radiative models. At
present time a considerable interest has been encapsulated to studying elementary
atomic processes in plasmas environments (for example, see [1–30] and Refs.
therein) because of the plasmas screening effect on the plasmas-embedded atomic
systems. In many papers the calculations of various atomic and ionic systems
embedded in the Debye plasmas have been performed [11, 12, 16, 29, 30]. Calculation of emission spectra of the plasmas ions based in the precise theoretical
techniques is practical tool, which may be used instead of very expensive sophisticated experiments. Nevertheless, there are known principal theoretical problems to
be solved in order to receive the correct description of master parameters of the
elementary atomic processes in laser, collisionally pumped plasmas. First of all,
speech is about development of the advanced quantum-mechanical models for the
further accurate computing oscillator strengths, electron-collisional strengths and
rate coefficients for atomic ions in plasmas, including the Debye plasmas. As
usually, a correct accounting of the relativistic, exchange-correlation, a plasmas
environment effects is of a great importance. To say strictly, solving of the whole
problem requires a development of the quantum-electrodynamical approach as the
most consistent one to problem of the Coulomb many-body system.
In this chapter we present the fundamentals of an advanced relativistic energy
approach, based on the Gell-Mann and Low formalism, to studying spectroscopic
characteristics of the multicharged ions in the Debye plasmas, in particular, computing the electron-ion collision strengths, cross-sections etc. The approach is
combined with relativistic many-body perturbation theory (PT) with the Debye
shielding model Hamiltonian for electron-nuclear and electron-electron systems.
The optimized one-electron representation in the PT zeroth approximation is constructed by means of the correct treating the gauge dependent multielectron contribution of the lowest PT corrections to the radiation widths of atomic levels. It is
worth to remind that the method of the relativistic many-body PT formalism is
constructed on the base of the same ideas as the well-known PT approach with the
model potential zeroth approximation by Ivanov-Ivanova et al. [31–44]. However
there are a few fundamental differences. For example, in our case the PT zeroth
approximation [51, 54] is in fact the Dirac- Debye-Hückel one. In order to calculate
the radiative and collisional parameters an effective gauge-invariant version of
56
A. V. Glushkov et al.