[en] In two previous papers we expressed the total energy of the spin multiplicities of a multi-fermionic system, within an orbit induced by a local-scale transformation with scalar function f(r), as an exact functional of the components of the single-particle density p(r). In this paper we provide an integral-differential equation implicit in p(r) and show how to solve it interactively using f(r). We also show how to derive a similar equation explicit in f(r) after expressing the total energy as a functional of f. (authors). 12 refs

[en] We show that, in the rigorous approach taking account of spin of the density functional theory, the spin correlation functions and matrices are entirely determined by the charge distribution density ρ(r). We form the multiplicities of spin distribution and correlation density functionals, from which the theory is extended to the degenerate states of a spinless Hamiltonian. We show that the spin correlations and the densities of spin pairs, spin-orbit interaction and spin-spin interaction are determined by the function ρ(r)

[en] Expressions for the reduced matrices and density functions of N-fermion systems of arbitrary order s (1<=s<=N) are derived within the frame of rigorous spin approach to the density functional theory (DFT). Using the local-scale transformation method and taking into account the particle spin it is shown that the reduced matrices and density functions are functionals of the total one-fermion density. Similar dependence is found for the distribution density of s-particle aggregates. Generalization and applicability of DFT to the case of s-particle ensembles and aggregates is discussed. 14 refs

[en] A semi-classical density functional (SCD) approach have been applied to the smoothly varying part of the Hartree-Fock (HF) binding energy in atoms of the first part of the periodic table. A comparison with the Thomas-Fermi-Schwinger (TFS) model shows that there are tiny differences between E_SCD and E_TFS consisting mainly in opposite drifts of the curves δE_SCD(Z) and δE_TFS(Z) with respect to the baseline. These drifts correspond to a non-oscillating term proportional to Z which is over-estimated in E_SCD but is missing in E_TFS. In the HF energy variation there exists a term proportional to Z³ and Z⁴ in addition to those coming from SCD and TFS models. The minima of both curves δE_SCD(Z) and δE_TFS(Z) are slightly shifted relative to the points of filling the shells and subshells in the periodic table. It is suggested that the resemblance of the HF energy third derivative to the curve of the first-ionization energies may connect the shell effects to electrons near the Fermi surface. 2 figs., 13 refs

[en] Expressions for the first- and second-order spatial matrices components and density function components, the matrix and the first-order spin density function of N-fermion systems of arbitrary order s (1<=s<=N) are derived within the frame of rigorous spin approach to the density functional theory. All these quantities are functionals of the single-electron density. It is shown that all two-particle correlations, the distributions of the single-particle spin density and spin angular momentum, the effects related to magnetic resonance are defined by the total single-electron density. 12 refs

[en] A rigorous approach taking account of spin of the density functional theory is presented. It is shown that the reduced density functions and matrices of any order (s=1,...,N) of an N-fermion system, as well as the spin density and distribution density of s-particle aggregates in the 4s-dimensional configuration space, are functions of the one-fermion density, and their form is presented

[en] We show that, in the rigorous approach taking account of spin of the density functional theory, the spatial components of the reduced density functions and matrices of orders 1 and 2 are functionals of the monoelectronic density. The same holds for the resulting charge and spin distribution and correlation densities. We present the mathematical form and discuss the physical meaning of these functionals. All biparticular correlations, as well as the spin distribution density and resulting magnetic coupling tensors, are entirely determined by the charge distribution density

[en] The present work deals with the effects induced by nuclear deformations and electron correlations on the electron ground-state energies of low and multiply charged helium like ions. Numerical calculations of the ground state energies including mass corrections and polarization of the electronic system have been performed for such heliumoid ions with nuclear charge number from Z=2 to Z=118. A perturbation method has been developed based on a variational principle using explicitly correlated two-electron wave functions. The mass-polarization term accounting for correlation effects has been included for the first time in the minimization procedure. These effects have been found to be particularly pronounced for ions corresponding to nuclear magic numbers. The present method provides a general framework for high-precision calculations of plasma diagnostics.

[en] In our investigations of interaction between electromagnetic field and matter experimental results were observed, which were grouped under the working name “Surface Photo Charge Effect” (SPCE). The important point is that the interaction of any solid with electromagnetic field induces an alternating electric signal with the same frequency as the frequency of the incident field [1]. The voltage between the irradiated sample and a second solid, whose potential is assumed to be zero, is measured contactlessly. The SPCE represents generation of an alternating voltage when a solid interacts with a modulated electromagnetic field. The potential difference between the irradiated sample and the common ground of the system is measurable and depends on many factors. The name Surface photo charge effect has been kept historically. It does not reflect the newer experimental results. (author)

[en] Multiply charged isoelectron Helium ions in high-temperature astrophysics and laboratory plasma possesses specific properties and characteristics caused by the noncompensated by electrons long-range Coloumb field of the nuclei. When the ion charge z increases, the relativistic effects role rapidly rises. The LS coupling turns into j − j coupling through area where these two couplings are equally probable - complex coupling. The mass polarization effects become less, but the role of the mass corrections is the same, ensuring the accuracy of the numerical results. The strong Coloumb field determines possibility one or two electrons to occupy highly excited quasidiscrete (autoionized) states, outside the ionization limit. There are two decomposition channels of the excited ion: autoionization and radiation. In that case one can observe several resonance processes, for example electron transition in bound (excited or ground) state with photon emission - radiative recombination (RR) and the opposite process - photoionization. In the case of electron capture the decomposition channels of double excited ion are two also: autoionization and radiation. Radiation decomposition is also possible to realize several resonance processes, depending on the energy electron capture. In the case of electron ”observer” the transition of ion’s electron from free to bound (excited or ground) state is accompanied by so called satellite lines in the spectrum. In the case of interaction with electron having the appropriate resonance energy, there is electron capture and simultaneous ion excitation. The radiative decomposition of double excited ion realizes by photon emission and electron transition into bound (excited or ground) state - dielectronic recombination (DR). In order to investigate the multiply charged ions in high-temperature plasma, theoretical calculations should account relativistic effects, but studying the scattering effects are solved applying non-relativistic approaches: the deformed waves method, strong coupling method, which at Z → ∞are leading to the classical Born-Coloumb approximation with exchange. The applying of these methods in the approaches for plasma diagnostic requires using of precise values for the energetic quantities of the final non-relativistic bound electron states. Then the resonance energy of the interacting electron is possible to be estimated. The proposed work presents ground state electron energies, mass corrections and mass polarization effects of He isoelectronic ions with nuclear charge for the main nuclides from Z = 2 to Z = 118. The developed analytical and numerical method in the Explicitly Correlated Wave Functions approach gives high accuracy of the numerical results, which allows direct application in precise approaches for plasma diagnostics. The dependence of the obtained energies versus Z is investigated, as well as the relative and complex contributions of mass corrections and mass polarization effects in formation of the nonrelativistic and relativistic ground state electron energies. The role of the mass polarization effects is investigated for transition from LS coupling, though complex coupling, to j − j coupling. (author)