Search

Branching ratios between the radiative single- and double-electron transitions into the doubly ionized K shell have been calculated in lowest order perturbation theory as a function of the atomic number. The results obtained are compared with the calculations of other authors and with the available experimental data.

Oscillator strengths and transition probabilities are obtained from an intermediate coupling scheme. The initial basis of the eigenstates is formed in LS -coupling. To obtain the resulting energy matrix, Z -1 perturbation theory is applied. The values of oscillator strengths and transition probabilities for 1 s 2 2 p 2 −1 s 2 2 s 2 p and 1 s 2 2 s 2 p −1 s 2 2 s 2 transitions are calculated and the comparison is made with some recent results. The nuclear charges ( Z ) involved varied from Z =4(Be(I)) to Z =35(Br(XXXII)).

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.

A theory for calculating energies and wavelengths using the Z-expansion technique is presented; it is suitable for degenerate autoionisation states of many-electron ions. The Hartree-Fock energy, correlation energy and relativistic corrections have been taken into account. To calculate the relativistic part the first non-zero term of the expansion in powers of Z alpha was considered, which, in fact, is described by the Breit Hamiltonian. Four-electron systems are considered as an example. Results of calculations of the wavelengths as well as the theory and numerical results for autoionisation rates and radiative transition probabilities will be given in future papers.

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.

An analysis was made of the intensities of satellites of the La resonance doublet of H-like ions with nuclear charges in the range Z = 12–16, corresponding to transitions from autoionizing doubly excited levels of He-like ions. Consideration of transitions of the ls2l'–2l2l' and 1s3l'–2l3l' types made it possible to integrate completely the spectrum of a laser plasma formed when the power density of the heating radiation was q ~ 1014 W/cm2. The agreement between the theory and experiment was good, with the exception of the intensity of the λ = 8.5305A line in the Mg spectrum.

S-matrix method leads to a complex expression for electron interaction energy. In the present paper the calculation of the imaginary energy part Gamma is given. The connection between the imaginary energy part and the magnetic and electric multipoles is established. Numerical calculations of transition probabilities and level lifetimes for the configuration 2p3p are made for ions with nuclear charge Z=5-45.

An analysis was made of the distribution of the relative intensities of spectral lines with a common upper level in transitions of the 2s2pk+1–2pk+2 type in N-, C-, B-, and Be-like ions of Ca, Ti, and Fe excited in a laser plasma and recorded photographically by a glancing-incidence spectrograph. Use was made of theoretically calculated transition probabilities. The relative spectral sensitivity of a DFS-6 spectrograph used in combination with UF-4 photographic emulsions was determined as a function of the wavelength in the range 100–250 A. It was found that the dependence is nonmonotonic. The results were used in some diagnostic applications to laser plasma spectra.

The first few terms of the perturbation expansions for the function and the energy shift of a degenerate state of an arbitrary quantum mechanical system are obtained using the adiabatic formula. It is shown how the expansion for the secular operator may be obtained from the expansion for the function. The results are used to calculate energies of the ground and some excited states and multiplet splittings of some beryllium-like 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.

Calculations of the wavelengths and transition probabilities of the radiative transitions 1 s 2 2 s 2 -1 s 2 s 2 2 p , 1 s 2 2 s 2 p -1 s 2 s 2 p 2 , 1 s 2 2 p 2 -1 s 2 p 3 and of the autoionization rates of the states 1 s 2 s 2 2 p , 1 s 2 s 2 p 2 , 1 s 2 p 3 for Be-like multicharged ions with Z = 6, 8, 10–42 have been made. Perturbation theory with inclusion of configuration mixing was used. Relativistic effects were considered in the limits of the Breit operator. The calculations were made in the intermediate coupling scheme.

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.

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.

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈HB>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s2 2sn1 2pn2 (2 ≧n1≧ 0, 6≧ n2 ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).

For pt.I see ibid., vol.12, no.19, p.3171 (1979). A theory for calculating autoionisation rates and radiative transition probabilities using the Z-expansion technique which is suitable for autoionisation degenerated states of many-electron systems is given. The autoionisation rates are considered as the imaginary part of the energies and are calculated in an analogous manner to the real part. Only the first non-zero term was taken into account. The calculations have been carried out for ions with 4-9 electrons and Z=6-30. The roles of correlation and relativistic effects are discussed. The importance of intercombination transitions is pointed out. The numerical results are given for the Be, N, O and F isoelectronic sequences.

Expressions have been obtained on the basis of S-matrix theory for the computation of electrical multipole transition probabilities in a relativistic approximation in a multielectron atom in first-order field perturbation theory. Also considered are corrections corresponding to simultaneously taking account of the external field and the interelectron interactions. Results of computing the wavelengths and probabilities of intercombinational transitions in multicharge ions between the configurations 1s 2p-1s2 for 4 ≤ Z ≤28 and 1s2\(2s^n 1 2p^{n_2 } - 1s^2 2s^{n_1 \pm 1} 2 p^{n_2 \pm 1} \) for20 ≤ Z ≤ 30 are presented. The data obtained can be used to interpret soft x radiation originating in transitions observed in the solar corona and high-temperature plasma laboratories.

'Itto different calculational methods (AUTOLSJ and MZ) are used to obtain the energy levels and autoionization probabilities for doubly excited states 29. 3i' of two-electron systems. A Z dependence of these parameters for an isoelectronic sequmce of He-like ions (6 < Z < 44) and a comparison between the results obtained by these two methods are presented.

The possibility of stimulated emission as a result of transitions in multiply charged neon-like ions is considered. The energies of excited terms with the 2p53s, 2p53p, and 2p53d configurations are calculated for ions with Z=4–17. The wavelengths of the expected laser transitions are given for the λ≈250–1600 A range.

The autoionization widths of levels 1s 2s 2pjJ, 1s2s22S1/2, and 1s2pj2pj′ J have been calculated for ions with Z = 6–30. The calculation has been carried out in intermediate coupling. The decay amplitudes have been calculated in a relativistic approximation.

The probabilities for two-electron-one-photon transitions to K and L shells with two vacancies have been calculated in the present paper on the basis of many-body perturbation theory for atoms and ions for a wide range of variation of the atomic number Z. All possible dipole correlated transitions of L and M electrons are considered and the influence of the number of L and M vacancies on their characteristics is investigated. The branching ratios of the one- and two-electron transitions: 1s-1-2p-1 and 1s-2-2s-12p-1, 2s-1-3p-1 and 2s-2-3s-13p-1 as well as 2p-1-3s-1 and 2p-2-3s-13p-1 have been calculated. The results obtained show that the branching ratio of one- and two-electron transitions of M electrons to the L shell with two 2s vacancies is strongly dependent on the population of the M1 subshell. And in the case of the 2p-2-3s-23p-1 transition the value of the ratio changes considerably with the number of vacancies not only in the M2,3 but also in the L2,3 subshells. The result is a strong sensitivity of the Z dependence of the characteristics of two-electron-one-photon transitions observed in ion-atom collisions to changes in the structure of the electron shells of colliding atomic systems.

Satellite lines of the Phosphorus H-like and He-like resonance lines have been observed in the DELPHiN plasma laser device at the Lebedev Institute in Moscow. Analysis of some wavelength ranges i s carried out by adjusting a theoretical spectrum to the observed one. Different plasma conditions (collisional radiative equilibrium or local thermodynamical equilibrium) are assumed to obtain a good f i t of various parts of the observed spectrum. A f i t t ing of the whole spectrum may be used to obtain a dens1 ty diagnostic. Satellite lines of the Phosphorous H-like and He-like resonance llnes have been observed in the DELPHIN plasma laser device at the Lebedev lnstitute of Moscow. This spectrum covers the 5.8A 7.4A wavelength range and corresponds to the f i rs t resonance line of the H-like system and to the first, second, thlrd and others resonance 1 ines of the He-like system and associated satellite 1ines.l t has been recorded simultaneously. The Nd-laser radiation is focused on a phosphorous plane target by an aspherical lens. The laser intensity reaches 5.1 014 w/cm2 and the plasma size, nearly spherical, i s 200 prn diameter.The geometry of the experiment i s such as to miniminize the effect of plasma motion and dimension on the line wldth and shift. For this purpose, a CaF2 crystal (2d=6.28& i s placed perpendicularly to the target. The experimental spectrum i s shown i n figure 1. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989164

On the basis of the S-matrix approach, a theory of perturbations in 1/Z is developed; the energy of a multielectron system is written in the form of a double series in powers ofα andαZ and a method of determining the coefficients of this series in a j-j coupling scheme is given. The method is applied to configurations of the type\(1s^2 2s^{n_1 } 2p_{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^{n_2 } 2_{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}^{n_3 } \), and numerical results are given for the wavelength of transitions between several states of the isoelectronic as sequence of carbon, illustrating the good agreement between experiment and theory.

The wavelengths, radiative transition probabilities, and autoionization rates have been calculated for ions with atomic numbers Z = 4 to 34. Transitions 2p-1s, 2p2l-1s2l, 1s2l-1s2, 1s2p2l-1s22l have been considered. Perturbation theory in 1 Z has been used.

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.

Wholly relativistic calculations of the transition probabilities in two-electron ions with arbitrary high nuclear charge Z are made. The Dirac one-electron functions and the exact electromagnetic interaction operator are used. All the transitions between the levels of the ground (1s)2 and excited 1s2s+1s2p configurations are calculated.

On the basis of the field form of perturbation theory energy levels of atomic systems with numbers of electrons up to 10 are calculated. Configurations 1s22sn12pn2 (n1=0-2, n2=0-6) are considered. The coefficients Delta E1, Delta E2 in the energy expansion by powers of 1/Z E=E0Z2+ Delta E1Z+ Delta E2+ Delta E3 Z/1... are calculated. Hartree-Fock energies are also represented in the form of a Z-expansion, and the coefficients Delta E1HF, Delta E2HF, Delta E3HF of this expansion are computed. These calculations allow us to represent the correlation energy in the form of a Z-expansion.

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.

We have previously [1] calculated diagram contributions for the f i r s t two orders of per turbat ion theory for the ground states and cer ta in excited states of light atoms. We have also given [2] numer ica l values for the contribution from d iagrams for s ta tes with fil led shells 1 and 2 together with one e lectron or one hole in shell n = 3. Here we consider s tates with two e lec t rons (holes) in shell n = 3.

The relaxation times of phenoxy radicals in KU-1 ionite resins were measured in the temperature range from 83 to 360‡ K as well as at 4.2‡ K. It was shown by comparison of the results obtained with the pulse and continuous saturation method that the theory of nonuniform broadening allows one to obtain accurate quantitative data. An algorithm is introduced for determination of the relaxation time of spin packets and the width of the distribution functions from the saturation curves obtained under conditions of slow passage.

The contributions from the diagrams of the first two orders are calculated for the energy of the ground state of Be. The result is E2= =−1.25 Z2+1.55927422 Z−0.8775, with E 2 corr =−0.01172683 Z −0.0720. Perturbation theories for the ground-state energy of Be are compared for Hartree-Fock and hydrogen-type functions.

Transition probabilities and oscillator strengths are calculated for the configurations 1s2 2sn1 and 1s2 2sn1-1 2pn2+1, which are, respectively, of the form P=a/Z (1+Τ/Z+⋯) andf=α/Z (1+Β/Z+⋯). Numerical values are given fora, Τ,α, andΒ.

Intercombination transitions 2s22p4 3P-2s2p5 1P0 in the oxygen-like ions from Fe to Zn are obtained in laser-produced plasma spectra. The relative intensities and the wavelengths of these transitions are in good agreement with calculated ones. The laboratory data obtained may be used for predicting the wavelengths of forbidden lines in solar flares.

Two different calculation methods are compared for Fe XXIII – Fe XIX spectra in the X-ray range between 1.85–2 Å, for transitions of the type 1s2sk2pn−1s22sk2pn−1. Wavelengths, radiative transition and autoionization probabilities as well as the intensity factors are compared. These parameters are given in order to diagnosis low density plasmas as found in solar flares and Tokamak devices.

Spectra in the narrow vicinity of the Mg xii resonance line at λ = 8.42 A were obtained aboard the satellites ‘Intercosmos-4, -7’ and the rocket ‘Vertical-2’, as well as from laser-produced plasma. The high resolution in solar and laboratory spectra made it possible to reveal a new spectral structure close to the Lα (Mg xii) line from both short and long wavelength sides. The main features were observed in all the spectra and were interpreted as a single or group of dielectronic satellite lines due to 2l3l′ → 1s3l″ transitions in the He-like ions according to theoretical calculations which were carried out by means of relativistic Z-expansion technique. The derived electron temperature of the emitting volumes seemed to be ≈ 3 × 106 K for laser plasma and about 6 × 106 K for the solar flares studied. The latter value is in good agreement with the temperature estimated with the help of the resonance line-to-continuum intensity ratios.

The wavelengths of inner-shell 1s-2p transitions in the ions Fe XVIII-XXIV have been measured in solar flare spectra recorded by the Naval Research Laboratory crystal spectrometer (SOLFLEX) on the Air Force P78-1 spacecraft. The measurements are compared with previous measurements and with recently calculated wavelengths. It is found that the measured wavelengths are systematically larger than the wavelengths calculated using the Z-expansion method by up to 0.65 mA. For the more highly charged ions, these differences can be attributed to the QED contributions to the transition energies that are not included in the Z-expansion calculations.