calibrated within the special ab initio procedure within the relativistic energy
approach [37, 38].
The most complicated problem of the relativistic PT computing the radiative and
collisional characteristics of the multielectron atomic systems is in an accurate,
precise accounting for the exchange-correlation effects (including polarization and
screening effects, a continuum pressure etc.) as the effects of the PT second and
higher orders. Using the standard Feynman diagram technique one should consider
two kinds of diagrams (the polarization and ladder ones), which describe the
polarization and screening exchange-correlation effects. The polarization diagrams
take into account the quasiparticle (external electrons or vacancies) interaction
through the polarizable core, and the ladder diagrams account for the immediate
quasiparticle interaction. The detailed description of the polarization diagrams and
the corresponding analytical expressions for matrix elements of the polarization
quasiparticles interaction (through the polarizable core) potential are presented in
Refs. [36, 45–50]. An effective approach to accounting for the polarization diagrams contributions is in adding the effective two- quasiparticle polarizable operator
into the PT first order matrix elements. In Ref. [36] the corresponding
non-relativistic polarization functional has been derived. More correct relativistic
expression has been presented in the Refs. [45, 46, 49].
2.2 Generalized Relativistic Energy Approach
in a Scattering Problem
In order to calculate different characteristics such as oscillator strengths and energy
shifts due to the plasmas environment effect, the electron-collision strengths, collisional excitation and de-excitation rates etc. we use an advanced generalized
relativistic energy approach combined with the relativistic many-body PT [28, 29,
49, 50, 67–70]. Here we briefly present the key moments of the method.
In the theory of non-relativistic atom a convenient field procedure is known for
calculating the energy shifts ΔE of degenerate states. This procedure is connected
with the secular matrix M diagonalization [33, 37]. In constructing M, the
Gell-Mann and Low adiabatic formula for ΔE is used. The secular matrix elements
are already complex in the PT second order (the first order on the inter-electron
interaction). Their imaginary parts are connected with the radiation decay possibility. It is important to note that the computing the energies and radiative transition
matrix elements is reduced to calculation and the further diagonalization of the
complex matrix M and determination of matrix of the coefficients with eigen state
vectors B
IK
ie, iv [33–36, 41, 42]. To calculate all necessary matrix elements one must
use the basis of the one-quasiparticle relativistic functions. In many calculations of
the atomic elementary processes characteristics it has been shown that their adequate description requires using the optimized wave functions and an accurate
accounting for the exchange-correlation effects. In Ref. [37] it has been proposed
Advanced Relativistic Energy Approach in Electron-Collisional …
59
approach [37, 38].
The most complicated problem of the relativistic PT computing the radiative and
collisional characteristics of the multielectron atomic systems is in an accurate,
precise accounting for the exchange-correlation effects (including polarization and
screening effects, a continuum pressure etc.) as the effects of the PT second and
higher orders. Using the standard Feynman diagram technique one should consider
two kinds of diagrams (the polarization and ladder ones), which describe the
polarization and screening exchange-correlation effects. The polarization diagrams
take into account the quasiparticle (external electrons or vacancies) interaction
through the polarizable core, and the ladder diagrams account for the immediate
quasiparticle interaction. The detailed description of the polarization diagrams and
the corresponding analytical expressions for matrix elements of the polarization
quasiparticles interaction (through the polarizable core) potential are presented in
Refs. [36, 45–50]. An effective approach to accounting for the polarization diagrams contributions is in adding the effective two- quasiparticle polarizable operator
into the PT first order matrix elements. In Ref. [36] the corresponding
non-relativistic polarization functional has been derived. More correct relativistic
expression has been presented in the Refs. [45, 46, 49].
2.2 Generalized Relativistic Energy Approach
in a Scattering Problem
In order to calculate different characteristics such as oscillator strengths and energy
shifts due to the plasmas environment effect, the electron-collision strengths, collisional excitation and de-excitation rates etc. we use an advanced generalized
relativistic energy approach combined with the relativistic many-body PT [28, 29,
49, 50, 67–70]. Here we briefly present the key moments of the method.
In the theory of non-relativistic atom a convenient field procedure is known for
calculating the energy shifts ΔE of degenerate states. This procedure is connected
with the secular matrix M diagonalization [33, 37]. In constructing M, the
Gell-Mann and Low adiabatic formula for ΔE is used. The secular matrix elements
are already complex in the PT second order (the first order on the inter-electron
interaction). Their imaginary parts are connected with the radiation decay possibility. It is important to note that the computing the energies and radiative transition
matrix elements is reduced to calculation and the further diagonalization of the
complex matrix M and determination of matrix of the coefficients with eigen state
vectors B
IK
ie, iv [33–36, 41, 42]. To calculate all necessary matrix elements one must
use the basis of the one-quasiparticle relativistic functions. In many calculations of
the atomic elementary processes characteristics it has been shown that their adequate description requires using the optimized wave functions and an accurate
accounting for the exchange-correlation effects. In Ref. [37] it has been proposed
Advanced Relativistic Energy Approach in Electron-Collisional …
59