Relativistic Oscillator Strengths Research Articles

Relativistic MCDF oscillator strengths for the 4 s2 1S0−4 s4 p3P1, 1P1 transitions in zinc isoelectronic sequence

Relativistic multiconfiguration Dirac-Fock (MCDF) transition energies and oscillator strengths are computed for both the allowed 4 s 2 1 S 0−4 s4 p 1 P 1 and forbidden 4 s 2 1 S 0−4 s4 p 3 P 1 transitions in the Zn I through Rb VIII spectra. In the computational approach, the intravalence correlation is represented through limited relativistic configuration mixing while the valence-core correlation is approximated by a core-polarization model. The results agree favourably with available experimental data, except for Se V and Br VI. Comparison is also made with other theoretical data and particularly with nonrelativistic, multiconfiguration Hartree-Fock results where both intravalence and core-valence correlation is treated through elaborate configuration mixing. The multiconfiguration Dirac-Fock calculations are performed by use of an “optimal level” scheme; for neutral zinc, an “average level” scheme is also employed, which allows a thorough comparison between these two schemes in oscillator-strength computations.

A multiconfiguration Dirac-Fock study of the 6s 21S 0−6s6p 3P 1, 1P 1 transitions in the Yb isoelectronic sequence

Relativistic excitation energies and oscillator strengths are computed for the 4 f 14 6 s 2 1 S 0-4 f 14 6 s6 p 3 P 1, 1 P 1 transitions in Lu II, Hf III and Ta IV spectra in the multiconfiguration Dirac-Fock scheme. A modest amount of relativistic configuration mixing is used to represent the intravalence correlation while the valence-core correlation is treated by a core-polarization approximation. For singly ionized lutetium, for which experimental energies are available, the contribution of different configurations to intravalence correlation in both initial and final states is studied in detail. The influence of the collapse of the 5 d orbital on the contribution of the 5 d6 p configuration to the excited 6 s6 p 3 P 1, 1 P 1 states in Yb I through Hf III spectra is also discussed. Ionization energies are predicted for the 6 1 S 0, 6 3 P 1 and 6 1 P 1 states in the Hf III and Ta IV spectra, relative to both the ground 4 f 14 5 d 2 D 3 2 and the excited 4 f 14 6 s 2 S 1 2 states of their parent ions. In addition, ionization energies for the 4 f 14 5 d 2 D 3 2 ground states as well as the positions of the lowest 5 d 2 D 5 2 , 6 s 2 S 1 2 and 6 p 2 P 1 2 , 3 2 excited states are predicted for the Hf IV and Ta V spectra.

Relativistic oscillator strengths for the Cs isoelectronic sequence and collapse of ⨍ and d orbitals

Model potential calculations have been performed to investigate the influence of valence-core electron exchange on oscillator strengths in the Cs isoelectronic sequence. It is demonstrated that inclusion of valence-core electron exchange in the model potential calculations of oscillator strengths for transitions involving orbitals which undergo the collapse phenomenon (usually d or f orbitals) is important and may modify the character of the transition (emission or absorption) due to the change in the relative positions of the states involved. In the collapse region, oscillator strengths for these transitions may also depend strongly on the form of the exchange approximation used. The reason for this influence is that valence-core electron exchange greatly facilitates the collapse phenomenon, thus affecting the positions of states and radial transition integrals. For transitions which do not involve orbitals undergoing collapse or occur in members of the isoelectronic sequence distant from the collapse region, the exchange effects, although still important are much weaker and good results may be obtained not only with a model potential employing empirically adjusted exchange but also for a simple, free from adjustable parameters, semiclassical exchange approximation.

Relativistic oscillator strengths and excitation energies for the ns21S0-nsnp3P1,1P1transitions. II. Cadmium isoelectronic sequence

For pt.I see ibid., vol.18, no.8, p.1533 (1985). Relativistic excitation energies and oscillator strengths for both the resonance transition 5s2 1S0-5s5p 1P1 and the intercombination lines 5s2 1S0-5s5p 3P1 in the cadmium isoelectronic sequence are computed in an approach which combines limited relativistic configuration mixing to represent intravalence correlation with a polarisation model to account for valence-core correlation. This approach is able to greatly reduce the discrepancies between the theoretical and experimental oscillator strengths for these transitions. A substantial part of the remaining discrepancy, particularly for ionised systems, can probably be attributed to uncertainties in the available experimental data. Systematic trends along the sequence in both the oscillator strengths and in the relative contributions of intravalence and valence-core electron correlation are discussed and compared with those obtained previously for the mercury sequence. It is found that for spin-allowed transitions the share of intravalence correlation increases for lighter (lower Z) homologous systems in corresponding ionisation stages, whereas that of core-valence correlation decreases. For the spin-forbidden transitions, however, both correlation contributions seem to increase for lower Z homologues in the same ionisation stages.

Relativistic oscillator strengths and excitation energies for the ns21S0-nsnp3P1,1P1transitions. I. The mercury isoelectronic sequence

Relativistic excitation energies and oscillator strengths are computed for both the resonance transition 6s2 1S0-6s6p 1P1 and the intercombination line 6s2 1S0-6s6p 3P1 in the mercury isoelectronic sequence. In the authors' approach to the correlation problem, limited relativistic configuration mixing which represents, intravalence correlation is combined with a polarisation model which accounts for valence-core correlation. Systematic trends along the sequence are discussed both the oscillator strengths and for contributions of intravalence and valence-core electron correlation. Theoretical ionisation potentials, corrected for relativistic and core polarisation effects, are predicted for 1S0, 3P1 and 1P1 states in the Po V, At VI and Rn VII spectra of the mercury sequence as well as for the 2S1/2 ground states in the Po VI, At VII and Rn VIII spectra of the gold isoelectronic sequence.

Relativistic oscillator strengths for the 6s21S0-6s6p3P1,1P1transitions in neutral mercury. A new approach to the correlation problem

A new approach to calculations of correlation effects is described and applied to neutral mercury. In this approach limited relativistic configuration mixing to represent intravalence correlation is combined with a polarisation model to account for valence-core correlation. Calculations without parameter adjustment give excitation energies and oscillator strengths for both the resonance transition 6s2 1S0-6s6p 1P1 and the intercombination line 6s2 1S0-6s6p 3P1 which are in good agreement with experiment.

Relativistic model-potential oscillator strengths and transition probabilities for [formula omitted] transitions in Eu(II), Tb(II), and Ho(II) in J 1 j coupling

The lowest 4ƒ n6s−4ƒ n6p transitions are studied for the Eu( II) ( n=7), Tb( II) ( n=9), and Ho( II) ( n=11) spectra, where the J 1 j coupling is an acceptable approximation. The relativistic radial integrals, required to evaluate the oscillator strengths and transition probabilities, are calculated with the model-potential method, which includes also core-polarization effects. The similarities observed in oscillator strengths for transitions with given Δ J but different J values are discussed and explained. The computer oscillator strengths are compared with those obtained with the Coulomb approximation and it is found that the latter are only 11–12% lower. The core polarization influence on oscillator strengths is also investigated and the 19–21% decrease in oscillator strengths due to this effect is predicted. This result may, however, be overestimated because of some deficiencies in our procedure.

Resonance and intermediate-coupling effects in electron scattering with highly charged ions. I. Collision strengths forFe24+,Se32+, andMo40+

A study of electron-impact excitation of highly charged ions in the helium isoelectronic sequence is reported. Nonresonant, intermediate-coupling collision strengths are computed for transitions up to and including the $n=3$ states. With the 13 fine-structure levels, i.e., $1{s}^{2}(^{1}S_{0})$, $1s2s(^{3}S_{1};^{1}S_{0})$, $1s2p(^{3}P_{0,1,2};^{1}P_{1})$, $1s3s(^{3}S_{1};^{1}S_{0})$, and $1s3p(^{3}P_{0,1,2};^{1}P_{1})$, there are 78 different inelastic transitions. Main calculations are carried out in the nine-state distorted-wave approximation including partial waves $l\ensuremath{\le}15$. Relativistic effects are taken into account in the Breit-Pauli approximation. Nine-state close-coupling calculations are also carried out for ${\mathrm{Fe}}^{24+}$ with $l\ensuremath{\le}4$ at a few energies for comparison (and for later work in paper II). Higher partial waves ($lg15$) are treated by the Coulomb-Bethe method using accurate relativistic eigenenergies and oscillator strengths for the target ions. The $Z$ dependence of the departure from $\mathrm{LS}$ coupling is investigated. Present results are in good general agreement with previous calculations where available, but some discrepancies are noted or clarified. Collision strengths are tabulated at energies from near the excitation energy of the $n=3$ complex to sufficiently high energies to enable rate coefficients to be computed. For transitions to the $n=3$ levels and for transitions where resonances are not important, the present values should yield reasonably accurate excitation rates (resonances are considered in paper II). The present data are required particularly for the analysis of observed spectra from high-temperature, high-density plasmas where the line intensities may depend on collisional redistribution among a number of excited $n=2$ and $n=3$ states.

Relativistic Hartree-Fock energies and oscillator strengths for some ions with ns2np ( n=4minus;6) ground-state configuration

The lowest s and p levels in the spectra of ions isoelectronic with gallium, indium and thallium Ge(II) through Se(IV), Sn(II) through Te(IV), Pb(II), and Bi(III) are studied using the relativistic single-configuration Hartree-Fock method. The ionization energies, fine structure intervals, sharp series line-strength ratios, and oscillator strengths are computed and compared with experiments. Deviations in line-strength ratios from statistical ratios are discussed. The influence on oscillator strengths of valence- core electron correlations (core polarization) is included within the single-configuration scheme and is investigated. It is found that, for sharp series transitions, core polarization is less important in ions isoelectronic with Ga, In, and Tl than in neutral systems and both core-polarization-corrected and uncorrected oscillator strengths agree with experiments within experimental errors. This good agreement proves that, for sharp series transitions, the relativistic single-configuration Hartree-Fock method yields acceptable results.

Systematic trends of the relativistic energy levels and oscillator strengths for electric dipole transitions within the ground complex of aluminium-like ions

Oscillator strengths for electric dipole transitions within the ground complex of the aluminium isoelectronic sequence have been calculated up to Np80+ using the relativistic parametric potential method. The electrostatic interaction between all states of the complex is explicitly introduced. The Z dependence of the f values throughout the sequence is analysed for the particular example of transitions between the odd levels J=1/2 and the even levels J=3/2. Intracomplex correlation effects and relativistic effects simultaneously become very important at a sufficiently high stage of ionisation, where it is no longer possible to represent the wavefunctions by a pure state in the jj coupling scheme. Numerous anticrossing effects appear in the complex; they give rise to several important irregularities in the trend of the f values. Therefore, simple theoretical arguments cannot be used ab initio to predict the evolution of the f values along the sequence; furthermore the interpolation of the results within the sequence is a somewhat difficult problem which calls for a previous analysis of the systematic trends of the energy levels.

Influence of core polarisation on relativistic oscillator strengths for lowest s-p transitions in Yb II-Hf IV spectra

The influence of polarisation of the core by the valence electron on single-configuration relativistic Hartree-Fock oscillator strengths for the 6S 2S12/-6p 2P degrees 1/2,3/2 transitions in the Yb II, Lu II and Hf IV spectra has been studied. The core polarisation effect is included by introducing a polarisation potential in the one-electron Hamiltonian and by employing the corresponding correction for the transition dipole moment operator in the transition matrix element.

Relativistic Hartree-Fock oscillator strengths for the lowest s→ p transitions in the first few members of the Rb(I) and Cs(I) isoelectronic sequences, with allowance for core polarization

Relativistic single-configuration Hartree-Fock oscillator strengths for the lowest ns 2 S 1 2 → np 2 P 1 2 , 3 2 transitions in the first few members of the rubidium ( n = 5) and cesium ( n = 6) isoelectronic sequences have been studied, both with and without allowance for core polarization. The effect of polarization of the core of the atom or ion by the valence electron is included by introducing a polarization potential in the one-electron Hamiltonian and by employing the corresponding correction for the dipole-moment operator in the transition matrix element. The results obtained compare well with available experimental data and indicate a significant influence of core-polarization effects on oscillator strengths. The behaviour of the oscillator strengths for the low Z part of the isoelectronic sequences is discussed.

Relativistic Hartree-Fock oscillator strengths for the lowest s→ p and p→ d transitions in the first few members of the Ag(I) and Au(I) isoelectronic sequences, with allowance for cope polarization

Relativistic, single-configuration Hartree-Fock oscillator strengths for the lowest ns 2 S 1 2 → np 2 P 1 2 3 2 and np 2 P 1 2 3 2 → nd 2 D 3 2 5 2 transitions in the first few members of the silver ( n = 5) and gold ( n = 6) isoelectronic sequences have been studied, both with and without allowance for core polarization. Core polarization is included by introducing a polarization potential in the one-electron Hamiltonian and by employing the corresponding correction for the dipole-moment operator in the transition matrix element. The results obtained are compared with available experimental data and the influence of core-polarization effects on oscillator strengths is discussed.

Influence of core polarisation on oscillator strengths along the copper isoelectronic sequence

The influence of core polarisation on relativistic oscillator strengths has been studied for the 4s2S12/-4p2P1/2,3/2 and 4p2P1/2,3/2-4d2D3/2,5/2 transitions along the copper isoelectronic sequence. Core polarisation effects are included in a relativistic Hartree-Fock method as well as in a relativistic semi-empirical model-potential approach by introducing a core polarisation potential in the calculation of wavefunctions and by employing the corresponding correction for the dipole moment operator in the transition matrix element. The results obtained are compared with available theoretical and experimental data and the influence of core polarisation effects is discussed.

Relativistic oscillator strengths for np2 → np(n + 1)s transition array of SnI and PbI spectra in jj and intermediate coupling

The relativistic oscillator strengths for the np2 → np(n + 1)s transition array as well as the lifetimes of levels of the np(n + 1)s configuration in SnI and PbI spectra were calculated in jj and intermediate coupling. The relativistic radial integrals were computed employing the wave functions obtained by a semiempirical approach which allowed for exchange effects. The results obtained are compared with existing experimental and theoretical data. The significance of intermediate coupling for oscillator strengths computations is discussed. The agreement with experiment is for the present semiempirical results generally better (particularly for the PbI spectrum) than for oscillator strength deduced from 'Optimized Hartree–Fock–Slater' transition probabilities, which were published previously.

Relativistic oscillator strengths for some transitions in Cu(I), Ag(I) and Au(I)

Relativistic oscillator strengths have been calculated for transitions in the principal, sharp and diffuse series of Cu(I), Ag(I) and Au(I) spectra. The computations have been performed by employing a semiempirical method which includes exchange and core-polarization effects. A comparison is presented for the calculated ⨍ ik values with experimental and other theoretical data. The influence of core-polarization effects on oscillator strengths is discussed.

Velocity and length forms of oscillator strengths and unitary transformations of quantum electrodynamics

A unitary transformation on the total Hamiltonian of quantum electrodynamics is shown to relate the length and velocity forms of both nonrelativistic and relativistic oscillator strengths. For the gauge-violating self-consistant Hamiltonian of the Hartree-Fock approximation, the conventional relation between length and velocity forms is an approximation to a general relation between interaction Hamiltonians connected by the unitary transformation. From the point of view of the unitary transformation, the velocity form is as reliable as the length form, and the forms of length formulas of relativistic and nonrelativistic oscillator strengths are identical.

Relativistic oscillator strengths forE1transitions in the argon isoelectronic sequence

The relativistic electric dipole oscillator strengths in length and velocity forms are calculated for a number of elements in the argon sequence. The transitions studied are $3{p}^{6}\ensuremath{-}3{p}^{5}\mathrm{nd}$ $(n=3, 4)$ and $3{p}^{6}\ensuremath{-}3{p}^{5}4s$. The ground state includes correlation due to the configuration $3{p}^{4}3{d}^{2}$ in computing $p\ensuremath{-}d$ transitions. Relativistic effects on line strengths are found to be important in the $\ensuremath{\Delta}n\ensuremath{\ne}0$ transitions even at low $Z$. The origin of these large relativistic effects for low $Z$ in the $3{p}^{6}\ensuremath{-}3{p}^{5}4l$ transitions are discussed.

Theoretical oscillator strengths III. Transitions in Au I, Hg II, Pb IV, and Bi V spectra

In the course of this investigation the relativistic oscillator strengths were calculated for some transitions in the principal, sharp, and diffuse series of the Au I, Hg II, Pb IV, and Bi V spectra. The radial integrals were computed employing the wave functions for the active electron obtained by a semiempirical approach which allowed for exchange effects. A comparison between the calculated line and multiplet f values and the other available experimental and theoretical data is presented. The influence of the relativistic effects on the oscillator strengths values for the transitions under consideration is discussed.

Theoretical oscillator strengths for some transitions in Si(II), Ge(II), Sn(II) and Pb(II) spectra

Calculations are reported of non-relativistic and relativistic oscillator strengths for the principal, sharp and diffuse series as well as some lifetimes in the spectra of singly-ionized silicon, germanium, tin and lead. The radial integrals were computed by employing the wave functions obtained from a semiempirical approach which included exchange effects (the semiempirical Xα method). Good agreement was obtained with available experimental and theoretical data. A comparison between non-relativistic and relativistic oscillator strengths confirms the importance of the spin-orbit interaction of the optical electron, as well as other relativistic effects for the oscillator strengths, even for the spectra of moderately heavy ions. Some systematic trends in the calculated oscillator strengths and line-strength ratios were investigated along the spectral series, as well as along the sequence of homologous ions.