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Reduced matrix elements and transition rates are calculated for all magnetic dipole (M1) transitions within 2l2l' configurations and for some 2l3l' - 2l2l' transitions in Be-like ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded M1 matrix elements. The calculations start with a (1s)2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states, and some n = 3 configurations. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for all 11 M1 transitions within 2l2l' configurations and for 35 M1 transitions between 2l3l' and 2l2l' states. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. The importance of negative-energy contributions to M1 transition amplitudes is discussed.

Absolute energies of the autoionizing states 1s2s22pn [LSJ] with n = 3–6, 1s2s2pn [LSJ] with n = 4–6 and 1s2pn [LSJ] with n = 5–6, and non-autoionizing states 1s22s2pn [LSJ] with n = 2–6, 1s22s2pn [LSJ] with n = 3–6, and 1s22pn [LSJ] with n = 4–6 were calculated for ions with a nuclear charge Z = 6–54 by using the 1/Z perturbation theory method. These states were considered as the states with one or few holes in the Ne-like core state 1s22s22p6. Relativistic corrections were taken into account in the frame of the Breit operators. The autoionization rates for the above-mentioned autoionizing states and ions were computed as well and are shown in grafic forms as Z-dependences. These new atomic data represent an important material, which can be used in different areas of atomic and plasma physics involving the study of multiply-charged ions.

Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 2s–2p electric dipole transitions in berylliumlike ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start with a 1s2 Dirac–Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficents. Second-order MBPT is used to determine the matrix elements, which are evaluated for the 16 possible E1 transitions. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order MBPT. The importance of virtual electron–positron pair (negative energy) contributions to the transition amplitudes is discussed.

Energies of the ten (2l2l') states of ions of the beryllium isoelectronic sequence are determined to second order in relativistic many-body perturbation theory starting from hydrogenic basis functions. Both the second-order Coulomb interaction and the second-order Breit-Coulomb interaction are included. Each diagram contribution is represented as a power series in Z. The leading term of each diagram gives the nonrelativistic limit which coincides with the contribution obtained starting with nonrelativistic basis functions. We obtain numerical data for the relativistic corrections for 2l states of Li-like ions and for (2l2l') states of Be-like ions.

Energy levels and autoionizing rates of 2lnl' (n = 3–12, l = 0–4) configurations for He-like ions with Z = 4–54 were calculated by using the Z expansion method. Relativistic effects are taken into account using the Breit–Pauli operators. The asymptotic dependence on n of the energy matrix is discussed for 2lnl' states. Intermediate coupling coefficients obtained after diagonalizing the energy matrices were also studied. It was observed that these coefficients change very rapidly with n and Z due to a redistribution of contribution between relativistic and correlation effects. As a result, all other atomic characteristics (radiative and nonradiative transition probabilities, branching ratios) display non-monotonous Z- and n-dependences with maxima and minima.

The excitation energies and the probabilities for radiative and radiationless decays of hollow atom states belonging to the 2s22p, 2s2p2 and 2p3 configurations have been calculated on the basis of perturbation theory method (1/Z-expansion) in a broad range of values of atomic number Z. Our results agree well with the first observation of these states and the theoretical and experimental results obtained recently for neutral Li atoms. It should be noted that the 1/Z expansion method gives more accurate results for ions than for neutral systems, because of the limited number of coefficients of 1/Z expansion calculated in this work. In this case the good agreement provided by our results for neutral system allows us to believe that our data for the same triply excited states with Z>3 should be used for prediction of new experiments with these states.

Energy levels, radiative transition probabilities and autoionization rates for CuXIX including the 1s22s22p53lnl' (n = 3 ÷ 8, l' ≤ n – 1) and 1s22s2p63lnl' (n = 3 ÷ 4, l' ≤ n – 1) doubly excited states were calculated using the multi-configurational Hartree–Fock method (Cowan code). Contributions of relativistic effects were discussed in comparison with data obtained by the multi-configurational Dirac–Fock method (YODA code). Application of the theoretical data for interpretation of experimental spectra obtained by double-electron capture in slow ion-atom collisions is discussed.

Energies of the low-lying excited states of six atomic systems with two electrons above the core (Mg I, Al II, Hg I, Tl II, Pb I, and Bi II) and three systems with three electrons above the core (Al I, Tl I, and Bi I) are determined to second order in relativistic many-body perturbation theory using frozen-core Dirac-Hartree-Fock orbitals as a basis set. In the present report, the Breit interaction is included to first order only. Diagonalization of the effective Hamiltonian is carried out using two methods: (I) the symmetric first-order Hamiltonian (including both Coulomb and Breit interactions) is diagonalized and then the second-order correlation is determined using the first-order eigenvectors; (II) the first-order (Coulomb plus Breit) together with the non-symmetric second-order effective Hamiltonian is diagonalized. Different model spaces are considered. Contributions from the three-electron interaction are compared with contributions from the two- and one-electron interactions. Comparisons with experiment are made.

The dielectronic recombination rate coefficients to the excited states for n = 2–6 are calculated including 1s22l2l'nl'' (n = 2–6, l'' ≤ (n − 1)). The values for the excited states higher than n = 6 are extrapolated and the total dielectronic recombination rate coefficients are derived. The rate coefficients to the excited states are fitted to an analytical formula and the fit parameters are given. The effective recombination rate coefficient for different electron densities are also derived.

We have calculated spectra due to Kα line emission from aluminum Li-, Be-, B-, C-, N-, O- and F-like ions. The following atomic processes have been taken into account to model the population distribution of the upper levels of these transitions: dielectronic recombination, and inner-shell collisional excitation and deexcitation. From these processes, inner-shell excitation is the dominant populating process. We illustrate this result by calculating and displaying the Kα emission spectra of B- and C-like Al produced under different conditions. These results are relevant for the interpretation of Kα emission spectra generated by plasmas with hot electrons.

Absolute energies of the autoionization states 1s2s22pn [LSJ] with n = 0–2, 1s2s2pn [LSJ] with n = 1–3 and 1s2pn [LSJ] with n = 2–4 and non-autoionizing states 1s22s22pn [LSJ] with n = 0–1, 1s22s2pn [LSJ] with n = 0–2 and 1s22pn [LSJ] with n = 1–3 were calculated for ions with nuclear charge Z = 6–54 by using the 1/Z perturbation theory method. Relativistic corrections were taken into account in the frame of the Breit operators. The autoionization rates for the above-mentioned autoionization states for ions with Z = 6–54 were computed as well. These data are very important for modelling the satellite spectra produced by high-temperature plasma with thermal and non-thermal electrons.

Two theoretical methods, namely perturbation theory of Z-expansion (MZ code) and multi-configurational Hartree-Fock methods (Cowan code), were used for identification of Coster-Kronig (CK) electron spectra from the singlet and triplet 1s22p9l states of S12+. The correlation effects are discussed through comparison between two methods. Transition energies have also been calculated for CK electron energy from 1s22pnl (n = 10–20) states.

Excitation cross sections and rate coefficients by electron impact were calculated for the 1s22s–1s2s2p, 1s22s–1s2s2 and 1s22s–1s2p2 transitions of the Li-like ions (C IV, N V, O VI, Ne VIII, Mg X, Al XI, Si XII, S XIV, Ar XVI, Ca XVIII, Ti XX, Fe XXIV, Ni XXVI, Zn XXVIII, Ge XXX, Se XXXII, Kr XXXIV and Mo XXXX) in the Coulomb-Born approximation with exchange including relativistic effects and configuration interaction. Level energies, mixing coefficients and transition wavelengths and probabilities were also computed. Calculations performed by the 1/Z perturbation theory and Coulomb-Born approximation are compared with the R-matrix method and the distorted-wave approximation were Z is the nuclear charge. Formulae obtained for the angular factors of n-electron atomic system allow one to generalize this method to an arbitrary system of highly charged ions.

The Feynman diagram technique was used to calculate the non-relativistic part of the energy of 1s23l3l' and 1s23l4l' states. The Hartree-Fock part of the energy was calculated by the Z-expansion method. The correlation part of the energy was obtained as the difference between these two energies represented in form of 1/Z series. The resulting data were compared with theoretical data obtained for the identification of electron spectra (1s23l3l' - 1s22l transitions).

Energy levels, radiative transition probabilities and autionization rates for C II including 1s22l2l'nl" (n = 2–6, l" ≤ (n − 1)] states were calculated by using the multi-configurational Hartree-Fock (Cowan code) method. Autoionizing levels above three thresholds: 1s22s2(1S), 1s22s2p(3P), 1s22s2p(1P) were considered. Branching ratios relative to the first threshold and intensity factors were calculated for satellite lines and dielectronic recombination rate coefficients for C II ions.

The energy of Li-like states 1s2lnl' regarding to high Rydberg series (n = 2-10) were calculated for ions with a nuclear charge Z = 5-54 by using a perturbation theory method (Z-expansion). Relativistic effects were taken into account by the Breit-Pauli operators. The asymptotic dependence on n for the energy matrix of the 1s2lnl' states was discussed. The intermediate coupling coefficients obtained after diagonalization of energy matrices were studied. It was found that the values of these coefficients are in a strong dependence on the values of n and Z due to redistribution between the contribution of relativistic and correlation effects. It should be noted that the other atomic characteristics such as radiative and nonradiative transition probabilities, branching ratios have a non-monotonous behaviour regarding to the values of Z and n with maxima and minima. Auger and transition energies were compared with other theoretical results and experimental data concerning the 1s2lnl'LSJ (n = 2-7) states for different ions with Z = 6, 7, 8, 16, 17 and 18.

For autoionizing levels converging to the N = 3 threshold of He-like ions with Z = 3–26, energies and widths obtained within the generalized diagonalization approach are compared with the results of S-matrix perturbation theory. The combined data for the expansion coefficients can improve the validity of spectral calculations. Autoionization decay amplitudes and widths are obtained using both unscreened and screened hydrogenic orbitals for the free electron, as well as in the first order in continuum Coulomb coupling. Terms of order 1/Z can be extracted to improve the perturbational data for autoionization amplitudes, involving both screening corrections and the first-order continuum coupling. The relative significance of various atomic interactions in evaluating autoionization decay amplitudes is discussed.

Calculations of energy levels of 1s22s22p5nl, 1s22s2p6nl (n = 3?6, l = s, p, d, f) configurations of Ne-like ions with Z = 20-60 have been carried out with use of an MZ program. The energy matrix in this method (1/Z method or Z?expansion) is represented in the form of a Z-expansion, where Z is the nuclear charge. Relativistic effects are taken into account in the framework of the Breit operator. The contributions of radiative and high order relativistic effects are also considered. The results of the calculations are compared with theoretical and experimental data.

The energies of the atomic systems 1s2s22pn and 1s22s22pn with n = 0-6 for Z = 18, 26 have been calculated using two methods: SUPERSTRUCTURE (including only the configurations of the complexes: 1s2s22pn + 1s2pn+2 and 1s22s22pn + 1s22pn+2) and perturbation theory (MZ). Nonrelativistic and relativistic parts of energy have been considered separately. Relativistic effects have been taken into account by the Breit-Pauli operators. Relativistic shift and splitting have been discussed.

Energy and autoionization rate for Be-like systems (1s2s22p, 1s2s2p2, 1s2p3) with Z = 6-42 have been calculated with two methods: AUTOLSJ (SUPERSTRUCTURE: including only the configurations of the complexes: 1s2s22p, 1s2p3 and 1s2s2p2) and (MZ) perturbation theory methods. Non-relativistic and relativistic parts of the energy have been considered separately. Relativistic effects have been taken into account by the Breit-Pauli operators. Non-relativistic and relativistic autoionization decay have been compared in the two methods, the contributions of 1s22s and 1s22p decay channels have been investigated.

Many body perturbation theory in conjunction with the screening method has been applied to calculate radiative transition energies of highly charged ions. In the formulas obtained the energy values are averaged over LSJ as a function of the number of electrons distributed in up to 27 subshells taking relativistic energy shifts into account. The introduction of approximate screening parameters for nonrelativistic and relativistic parts of the energy allows us to limit our calculation to first order interelectron interaction only. The derived formulas have been proven to be very useful calculating X-ray spectra of Xeq+ (q = 44−48) ions interacting with the Cu surface. Comparison is made with other methods such as Hartree-Fock-Pauli (HFP), and relativistic model potential. Computational problems introducing different screening constants and asymptotic limits as well as contributions of the neglected second order interaction are discussed.

Excitation collision strengths, cross-sections and rate coefficients by electron impact are calculated for the transitions among 1s22s2, 1s22s2p, 1s22p2 levels of Be-like system of O V, Si XI, Fe XXIII and Mo XXXIX ions by Coulomb-Born approximation with exchange including relativistic effect and configuration interactions. The theoretical method for calculation is described and the results are compared with previous calculations. Numerical data and comparison are presented in tables as well as in figures. Two kinds of fitting formulae for cross-sections and rate coefficients are discussed.

The calculation of the energy of Ne-like ions was carried out on the basis of the model potential method. Possibilities and advantages of the method are discussed. Calculated results were obtained for the states 1s22s2p63l with l = s, p, d. The comparison with another calculation and experiment is presented for the ions with Z = 30, 34, 36, 39, 47, 49, 54. Z-dependencies of the energy levels are discussed. Transition probabilities and oscillator strengths were calculated for all types of transitions (2-3, 2-2, 3-3). The comparison of this calculation with other theoretical calculations was carried out for the ions with Z = 30, 34, 36, 39. Questions about level transpositions are discussed. Results of asymptotic approximation and direct calculations are compared for line strengths of the transitions 2-2 and 3-3 (S) for the ion U82+.

The perturbation theory on the relativistic basis has been applied to calculate the energies of two-electron systems. The results for the energy of noninteracting electrons have been taken from the work by Johnson and Soff. For the first order both a precise calculation has been made and an αZ-expansion has been obtained. For the second order a precise calculation of the nonrelativistic limit is available, i.e. that of the first term of the αZ-expansion. Subsequent terms of the αZ-expansion have been evaluated on the basis of the screening constant method. General formulae for the first and second orders for any states of a two-electron system are given. Numerical results of the ionisation potential are given for the states 1s2½, 1s½ 2s½, 1s½ 2pj with Z = 10-100.

Relative intensities of dielectronic satellite lines determined by radiative transition probabilities and autoionization rates are calculated for transitions 1s2lnl'-1s2nl', 1s2lnl'-1s22l (n = 4-10, l = 0-3) for Li-like ions with Z = 5-54 by using the perturbation theory method (Z-expansion). Relativistic effects are taken into account by the Breit-Pauli operators. It was observed that the relative factor intensity changes very sharply with n and Z due to redistribution between contributions of relativistic and correlation effects.

Energies of 2s23l, 2s2p(1P)3l, 2s2p(3P)3l and 2p23l states (with l = s, p, d) for B-like Na are calculated. These perturbation-theory calculations make use of a frozen-core relativistic Hartree-Fock basis sets. The calculations include Coulomb and Breit contributions from first- and second-order diagrams for both diagonal and non-diagonal matrix elements. Corrections for the frequency-dependent Breit interaction are taken into account in lowest order and corrections for the Lamb shift are also included. Contributions from three-electron diagrams are compared with those from one- and two-electron diagrams. Comparisons are made with available experimental data; we find good agreement in most cases with experimental term-splitting values in ions with small nuclear charge.

Energies of the 2s3s (1S0, 3S1), 2s3p (1P1, 3PJ), 2s3d (1D2, 3DJ), 2p3s (1P1, 3PJ), 2p3p (1S0, 3S1, 1P1, 1D2, 3PJ, 3DJ) and 2p3d (1P1, 1D2, 1F3, 3PJ, 3DJ, 3FJ) states of Be-like ions with nuclear charges Z = (4, 5,..., 30, 54) are determined to second order in relativistic many-body perturbation theory. Both the Coulomb interaction and the Breit interaction are included. Corrections for the frequency-dependent Breit interaction are taken into account in lowest order; corrections for the Lamb shift are also estimated and included. Comparisons with experiment and with other theoretical calculations are made. For ions with low nuclear charge, we obtain excellent agreement for the term-splitting. Results for the 2p-3d excitation energy of Xe+50 also agree very well with experimental measurements.

Calculations of energies and lifetimes of levels for configurations 2s22p53l and 2s2p63l were performed for the Mg, Si, S, Ar, Ca, Ti, V, Cr, Fe, Ni ions. The intermediate coupling scheme was used. The initial energy matrix was derived in the LS-scheme. Relativistic corrections were calculated using the Breit operator. Calculations were made in the framework of the Z-expansion perturbation theory.

Measurements and calculations of 3-2 transitions in Ne-like highly charged ions were performed. The measurements have been carried out for ions with nuclear charge Z = 39-60 excited in a low-inductance vacuum spark plasma. The Z-expansion and two versions of model potential methods were used in our calculations for all ions with Z = 36-92. A comparison of all available theoretical and experimental data for these transitions were made (Z ≥ 38). Recommended wavelengths which can be useful for identification of 3-2 spectra of Ne-like ions are given.

Satellite structure of the spectrum resulting from the consideration of configurations mixing was studied. These are the transitions of the type 1s2s22pn-1s22pn+1 and 1s2pn-1s22s22pn-3. Transition energies (eV) and probabilities (1013 s-1) were calculated for all possible values of n. The perturbations theory by 1/Z was used in the calculations. Relativistic effects were taken into account within the frames of the Breit operator. The obtained numerical values of transition probabilities are averaged over J, J' (Tables I-IV) and then over LS, L'S' (Table V). Minimum and maximum energies of transition being studied are given for transition energies (E). Numerical results are presented for Mg, Al, Si ions.

The specified calculation of wavelengths of resonance transitions in He-like ions (Z = 16-39) is compared with the results of the X-ray measurements in the spectra of low-inductance vacuum spark in the present paper. The calculation was made by Z-expansion method in the screening representation with the inclusion of relativistic and radiative effects. The experimental data have been obtained with compensation of the Doppler shift and taking into account the correction caused by the presence of adjoining satellites with n = 3. A slight difference between the theory and the experiment in the region Z = 38, 39 has been found.

Ionization potentials of 2 3PJ, 2 1P1, 2 3S1, 2 1S0 states are calculated. Relativistic and radiative effects are taken into account. Non-relativistic energies are calculated in the framework of the Z-expansion perturbation theory. Results for ionization potentials and wavelengths of transitions 1 1S0-2 1P1, 1 1S0-2 3P1, 1 1S0-2 3P2, 1 1S0-2 3S1 are given for ions with Z = 10-42.

The Z-expansion method for calculation of atomic characteristics is discussed. The calculation is performed for different autoionization states: Two-electron (2lnl'); three-electron (is2lnl') are given, Z-dependences of atomic characteristics, influence of relativistic and radiative effects are considered. All results are obtained by different programs: MZ, MCHF, MCDF, SUPERSTRUCTURE. Possibilities of each of the programs are discussed. For the satellite spectra of H- and He-like ions, theoretical and experimental data are compared. For satellite spectra of Ne-like ions, analytical formulae are given for transition energies and for probabilities of radiative transitions and nonradiative decays as functions of the number of electrons in the systems being considered.

The perturbation method for calculating atomic energies by power series in 1/Z and αZ has been extended to include parameters for screening and for expansion in the principal quantum number n. Numerical results are given and compared with observations for 1s nl and 1s2 nl of the helium and lithium isoelectronic sequences.

Two different methods have been used for a theoretical investigation of the energy spectra as well as transition probabilities of 2s 22p 2-2s2p 3-2p 4 in the case of Ca XV and Fe XXI: the non-relativistic Hartree-Fock method with relativistic corrections in the Breit approximation and the first two orders of a perturbation expansion in powers of 1/Z. Calculations are made in intermediate coupling using LS basis functions. Eigen-functions and eigenvalues of the Hamiltonian considered as well as wave-lengths and transition probabilities are presented in tables. The data obtained show that both methods lead to results which are in good agreement with the available experimental information. The results given can be used for the identification of energy levels not yet observed.