[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] The matrix elements and expectation values of the operators of the hyperfine electron-nuclear interactions in many-electron systems are presented in an analytical form, which can be applied for numerical calculations in the density matrix methods. The electron-nuclear spin-spin and contact interactions are considered,as well as the interaction between nuclear-spin and electron orbital motions. These interaction which take part in the effective Breit-Pauli Hamiltonian,determine hyperfine structure of the basic effects in the spectroscopy,which can be observed for example in electron spin resonance (ESR) and nuclear magnetic resonance (NMR) experiments

[en] The matrix elements and expectation values of the hyperfine interaction operators are presented in a form suitable for numerical implementation in density matrix methods. The electron-nuclear spin-spin (dipolar and contact) interactions are considered, as well as the interaction between nuclear spin and electron-orbital motions. These interactions from the effective Breit-Pauli Hamiltonian determine the hyperfine structure in ESR spectra and contribute to chemical shifts in NMR. Applying the Wigner-Eckart theorem in the irreducible tensor-operator technique and the spin-space separation scheme, the matrix elements and expectation values of these relativistic corrections are expressed in analytical form. The final results are presented as products, or sums of products, of factors determined by the spin and (or) angular momentum symmetry and a spatial part determined by the action of the symmetrized tensor-operators on the normalized matrix or function of the spin or charge distribution.

[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)

[en] Multiply charged Helium ions are strongly responsible for the properties and characteristics of high-temperature astrophysical and laboratory plasma, as well as for the processes within plasma. Our previous works [1–3] present ground state electron energies, mass corrections and mass polarization effects of He isoelectronic ions, with charge from Z = 2 to Z = 54. Results were obtained by solving the two-electron Schrödinger equation in the explicitly correlated wave functions (ECWF) approach. The numerical procedure brings to a solving of algebraic system of non-linear integro-differential equations of 4th order. 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 same type generalized Hylleraas’ ECWF are used. The variational procedure for determination of the coefficients is discrete, leading to an eigenvalue problem. The developed analytical and numerical method allows to obtain numerical results, which are practically coinciding with those presented in [4,5]. Using of the same method, we have the same accuracy for ions with charge Z > 10. 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 ground state electron energies. The approach developed may be regarded as a base for investigation of the relativistic corrections and QED effects at next stage. The accuracy of the obtained results allows directly usage in precise theoretical approaches [6,7] for plasma diagnostics.

[en] The non-relativistic energy magnitudes for the ground state of He and He isoelectronic series with atomic number Z = 3 ÷ 54, are calculated. Calculations are performed using an explicitly correlated trial wave-functions of the generalized Hylleraas type. We have developed a variational procedure that allows solving the two-particle Schroedinger equation for a practically unlimited number of parameters in a series of trial wave-functions along the positive degrees of Hylleraas coordinates. Non-conventional optimization methods are developed and particularly applied nonlinear programming is used to solve the problem. The contributions to the energy for various parameters is analyzed. The so-called mass-corrections and mass-polarizations to the non-relativistic energy is also studied. The obtained results are compared to existing experimental data and available data given by other authors. One should note that up to now such data have been computed only for atomic numbers Z = 2 ÷ 12. Behavior of the ground state energy versus Z, the effects of mass corrections and mass polarizations, as well as the contribution of these effects in formation of the electron system energies, are investigated.