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Transition probabilities of two-electron nd8(n + 1)s2-nd9(n + 1)p transitions and radiative lifetimes of nd8(n + 1)s2 states are investigated theoretically and experimentally. The theoretical results are obtained by the Hartree-Fock method and the measurements are performed by a delayed-coincidence method with pulsed electron excitation of investigated levels.

A simple general method is presented whereby measured spectroscopic energy-level data can be used to empirically construct the eigenvectors of intermediate coupling for an arbitrary configuration. These empirical eigenvectors can be used to elucidate the transition rates into, out of, and among the levels of the configuration by separating the effects of intermediate coupling from the radial transition moment. Predictive applications to the ${\mathit{np}}^{3}$ configurations of the N and P isoelectronic sequences are presented.

A new method for finding non-relativistic and relativistic wave-functions of an electron moving in the field of a nuclear charge in the jj coupling scheme is proposed. It is based on the usage of generalized spherical functions. The mathematical apparatus necessary to find the expressions for matrix elements of the non-relativistic and relativistic energy or electron transition operators is developed. The formulas obtained for these matrix elements are more convenient than those usually used in jj coupling scheme; only their radial integrals and some phase multipliers depend on orbital quantum numbers.

It is shown that the isospin formalism is convenient for discussing the properties of the wavefunctions of the configurations n1lN1n2lN2 with respect to the orthogonal transformations of the radial orbitals. The main point of this formalism consists of the statement that the existence of an electron in one of the two shells n1lN1 or n2lN2 is considered as the additional degree of freedom in some abstract 'isospin' space. The corresponding basis is defined and the properties of the wavefunctions and operators are studied in this basis. The authors analyse the conditions under which the isospin T may be a fairly exact quantum number for complex electronic configurations.

The isospin basis is put into operation for investigation of atomic configurations, having two shells of equivalent electrons, characterized by the same orbital (LS coupling) or total (jj coupling) angular momenta of each electron. Tensorial properties of both the operators and the wave functions are studied in this basis. The two-particle operator is expressed in terms of the tensors irreducible in the isospin space. The problem of the additional classification of the levels is considered. The accuracy of the quantum numbers of the isospin basis in jj coupling scheme is discussed.

General expressions (both relativistic and non-relativistic) for the electric multipole transition operators, having not specified values of the gauge condition of the electromagnetic field potential, are presented. The dependence of oscillator strengths for electric dipole transition on the gauge is studied. In the general case it has the form of a parabola. The coefficients of the equation, describing this curve, as well as the values of the gauge for which the oscillator strength equals zero are expressed in terms of the length and velocity forms of the electric dipole transition operators. Transitions in Be-like ions are considered and the results of the calculations are compared with experimentally determined oscillator strengths.

Some principal problems of theoretical studies of the structure and spectra of complex many-electron atoms and ions, having as a rule several open electronic shells, are surveyed. The usage of various approaches is discussed while calculating energy spectra of the systems mentioned, including the relativistic version of least squares fitting method. It is shown that for many cases the spectra cannot be classified with the help of LS coupling scheme. The method of optimization of coupling scheme is described. The role of group-theoretical methods, namely, the groups of quasispin and isospin as well as the direct usage of corresponding Clebsch-Gordan coefficients, in theoretical atomic spectroscopy is emphasized.

Quantum-electrodynamic perturbation theory is used to investigate the relativistic energy of a many-electron atom. The corresponding formulae are reduced to a quite convenient form in which only radial integrals and phase multipliers depend on 1s22sp2 and 1s22p3. They are in fairly good agreement with experimental data.

The authors calculate the relative intensities of the recombination lines of the C II and N III ions. The observed intensities of these lines in the spectra of planetary nebulas are used to determine the abundances of the C III and N IV ions in 12 nebulas. The mean abundances of the C III and N IV ions for the considered planetary nebulas are found to exceed the total C and N abundances on the Sun: C/H = 4.2 x 10/sup -4/ and N/H = 0.9 x 10/sup -4/.

In this paper, the energy levels, wavelengths and transition probabilities have been calculated for some astrophysically important lines of the ions C II, C III, N III, N IV, O IV, and O V. These quantities are subsequently used to calculate the line intensities of these ions and to determine the abundance of the ions of carbon, nitrogen, and oxygen in a number of planetary nebulas. Single-configuration Hartree-Fock calculations are used in this paper to obtain the greater part of the transition probabilities and were made using the programs described. The examples given show that the configuration superposition method using the transformed functions make it possible to take into account the greater part of the correlation effects and find fairly accurate transition values.

The relativistic electric multipole transition operators are considered, not specifying the gauge condition of the electromagnetic field potential. The nonrelativistic limit of the relativistic expressions obtained is found. The relativistic corrections to various forms of the electric dipole transition operators are investigated. The electric multipole transition operator contains an arbitrary parameter, the gauge constant, dependence on which can serve as one of the criteria for the accuracy of the wavefunctions used. Calculated examples of the theory, starting with the general expressions found, are presented. The methods described and the formulae presented allow the authors to investigate in an effective way the electric multipole transitions for atoms and their isoelectronic sequences, including very highly ionised atoms.

A new modification of the theory of many-electron atoms is described in which tensorial properties of the quasi-spin operator are taken into account. The properties of tensorial operators, including the second quantisation operators, and their reduced matrix elements are studied with respect to quasi-spin space in the case of jj coupling in a shell of equivalent atomic electrons. The methods of angular momentum theory are generalised for the quasi-spin space. The properties of the wavefunctions and the coefficients of fractional parentage are studied with respect to quasi-spin space. Redmond's formula is generalised. Algebraic expressions for the wavefunctions and coefficients of fractional parentage are found for the shell jN(j

The method of the relativistic investigation of the energy spectra and the electronic transitions in the case of complex configurations, based on the theory of the irreducible tensorial operators and the genealogical coefficients, is described. The use of the quasispin and isospin technique in the relativistic approximation is discussed. Expressions are presented for electric multipole transition probabilities for general values of the gauge condition of electromagnetic field potential.

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.

Spectra of the ions Fe XVIII to Zn XXII, Ge XXIV and Se XXVI of the F I isoelectronic sequence were obtained. Identification of 156 spectral lines for the ions considered was made on the basis of a comparison of experimental wavelengths and relative intensities with theoretical wavelengths and transition probabilities. The lines identified belong to transitions between configurations 1s22s22p5-1s22s22p43d and 1s22s22p5-1s22s22p43s. Theoretical calculations were made using the Hartree-Fock method with the inclusion of spin-orbit interaction.

The mirror reflection symmetry which consists in the correlation of the substitution j −j −1 with the reflection of the coordinate system and of m −m with the reflection of the space with respect to the xy-plane has been applied to the quasi-spin formalism. The phases of the wave functions of the shell of equivalent atomic electrons treated as partially filled, as they relate to those when the same shell is treated as almost filled, have been established. The mirror reflection symmetry has been generalized for the supplementary quantum numbers used for distinguishing the terms of the same kind. The phases of the coefficients of fractional parentage of almost filled shell enabling us to determine them from those of partially filled shell have been specified. Corresponding phase relations for the matrix elements of operators have also been considered.

At present the number of papers in which many-electron atoms and ions are studied both theoretically and experimentally is increasing rapidly. The greatest attention is paid to the multiple-charged ions, observed both in astrophysical and laboratory high-temperature plasma. They are particularly important in the investigation of the solar spectra in the short wavelength region as well as in the study of the thermonuclear fusion.