Relativistic Multiconfiguration Hartree-Fock Research Articles

The Electric Dipole Transitions of Hydrogen Like Nobelium

It is an occasion to understand and test the methods for determination of atomic structure on hydrogen like ions especially with high atomic number, Z. Many studies such as interpretation of astrophysical spectra and atomic collision studies, the development of X-ray lasers etc. demand exact transition parameters data. This need is a reason of the present paper to support more precise atomic data of electric dipole transitions parameters for hydrogen like nobelium (No 101+ , Z=102). The wavelengths, logarithmic weighted oscillator strengths and transition probabilities of No 101+ have been reproduced with relativistic multiconfiguration Hartree-Fock (MCHF) and fully relativistic multiconfiguration Dirac-Fock (MCDF) methods. The transitions between nl ( n =1-9 and l =0-4) levels have been investigated in this work. The results of MCHF and MCDF methods have been compared with a unique theoretical work, because there has been neither theoretical nor experimental work in available literature.

Radiative lifetimes along even-parity J = 1, 2 Rydberg series of neutral tin

Using the time-resolved laser-induced fluorescence (LIF) technique in a tin atomic beam, 40 natural radiative lifetimes have been measured for the even-parity \(J = 1~5\)pnp (n = 10–13, 15–19) and \(J = 2~5\)pnp (n = 10–13, 15–19, 27, 31, 32), 5pnf (n = 4, 5, 9–19, 22, 23) levels along the Rydberg series and for all the 5p8p perturbing levels of neutral tin with energies in the range 52263.8 to 59099.9 cm-1. A two-step laser excitation scheme was used in the experiment. A multiconfigurational relativistic Hartree-Fock (HFR) calculation taking core-polarization effects into account has also been performed for the even-parity states for testing the ability of this approach to correctly predict the radiative properties of tin atom. Through an analysis of the energy levels structure by the multichannel quantum defect theory (MQDT), the channel admixture coefficients have been obtained and used to fit the theoretical lifetimes to the experimental ones in order to predict new values for the levels not measured. A generally good overall agreement between experimental and theoretical MQDT and HFR lifetimes has been achieved except for a few levels.

Radiative lifetimes and transition probabilities in Hf I and Hf III

Radiative lifetimes of nine odd levels in Hf III (5d6p 23 P 0,1, z 1 D 2 , z 3 D 1,2,3 , z 3 F 2,3,4 ) and of two odd levels in Hf I (5d6s 2 6p z 3 D 2,3 ) have been determined using Time-Resolved Laser-Induced Fluorescence. The investigated levels in Hf I were excited in a single-step process from the ground term (5d 2 6s 2 a 3 F), whereas in Hf III we started from either the ground term 5d 2 a 3 F or the low-lying 5d6s a 3 D term. For all of the investigated levels, the lifetimes have been measured for the first time. A multiconfiguration relativistic Hartree-Fock method, including core-polarization effects, has been used to compute radiative lifetimes of 15 Hf III levels, including those measured in this work. Transition probabilities for 55 transitions in Hf III are also given.

Radiative decay data for highly excited Zr i levels

Radiative lifetimes of 17 excited levels in Zr I, in the energy interval 29 000–40 974 cm −1 , have been investigated using the time-resolved laser-induced fluorescence method. The levels belong to the 4d 2 5s5p, 4d 3 5p and 4d5s 2 5p electronic configurations and were excited in a single-step process from either the ground term, 4d 2 5s 2 a 3 F, or from the low-lying 4d 2 5s 2 a 3 P and a 5 F terms. For three levels, we confirm previous measurements while for 14 of the levels the lifetimes have been measured for the first time. The experimental results are compared to theoretical calculations performed with a multiconfiguration relativistic Hartree–Fock method including core-polarization effects. Theoretical transition probabilities of astrophysical interest, scaled by the experimental lifetimes, for the depopulating channels of the investigated levels are also presented.

Radiative lifetime and transition probabilities inCdIandCdII

Radiative lifetimes of 11 levels belonging to the 5s5p P-1(1)o 5snd D-3(1,2) (n=6-9) and 5sns S-3(1) (n=7,8) series of Cd I, and of 5 levels of Cd II (i.e., 4d(10)5p P-2(1/2.3/2)o, 4d(10)6s S-2(1/2), and 4d(10)5d D-2(3/2,5/2)) have been measured using the time-resolved laser-induced fluorescence technique. Free neutral and singly ionized cadmium atoms have been generated by laser ablation. Single- or two-step excitation processes were considered to populate the levels under study. Branching fractions of Cd II transitions have been measured by laser-induced breakdown spectroscopy. Transition probabilities and oscillator strengths for Cd I and Cd II spectral lines originating from the above states as well as from the 4d(9)5 s(22)D(3/2,5/2) states of Cd II have been deduced by combining the experimental lifetimes and theoretical branching fractions obtained in multiconfigurational relativistic Hartree-Fock calculations taking core-polarization effects into account. (Less)

Observation of dielectronic satellites in the K-spectrum of argon ions in plasma produced by femtosecond laser pulses

The satellite structure of 1s2p1,3P1-1s21S0 lines of the He-like argon ion in plasma produced by a 45-fs laser pulse in a gas-jet cluster target is measured with a high spectral resolution. Radiation transitions 2p → 1s from autoionizing states (AISs) are detected for ions ranging from Li-like to F-like. The spectrum observed is theoretically simulated with the use of the spectroscopic data for the AISs of multicharged ions obtained within the multiconfiguration relativistic Hartree-Fock method. Good agreement with experimental data is obtained when the main population channels of these states are taken into account for typical values of cluster-target plasma parameters.

Time-resolved laser-induced fluorescence lifetime measurements and theoretical transition probabilities in Tb III

Lifetimes of four short-lived levels belonging to the ${4f}^{8}{(}^{7}F)6p$ configuration of Tb III have been measured using a two-step excitation time-resolved laser-induced fluorescence technique. They agree quite well with multiconfigurational relativistic Hartree-Fock calculations performed with inclusion of core-polarization effects. Using the experimental lifetimes and the theoretical branching fractions, a set of transition probabilities has been deduced for this ion.

Dielectronic recombination from Fe like Au^53+ to Ga like Au^47+ ions*

Ab initio calculations of the rate coefficients for dielectronic recombination from Felike Au53+ to Galike Au48+ ions are performed based on Cowan's quasirelativistic multiconfiguration HartreeFockRelativistic code and distorted wave approaches. A large number of single excited states and doublyexcited states are included in the present calculation. Because of the extensive distribution of autoionization state energy levels and complicated cascade effects, the dielectronic recombination rate coefficients at higher Z are different from those at lower Z's. The results indicate that the error between our work and other theories is less then 10% in the diagnosed electron temperature and density. It is feasible to simulate the average ionized state and charge state distributions in a well characterized highly ionized Au plasma.

Article

When the one-body part of the relativistic Hamiltonian H is asum of one-electron Dirac Hamiltonians, relativistic configurationinteraction (CI) calculations are carried out on an ad hocbasis of positive-energy orbitals, {u+j; j=1,2,...,m}, andmore recently, with the full bases of positive-energy andnegative-energy orbitals, {u+j ,u-j ;j=1,2,...,m}. Therespective eigenproblems,H+C+k=E+kC+k, k=1,2,..., N(m),andHCk=EkCk ; k=1,2,...,N(2m)are related throughE+k <= Ek+N(2m)-N(m)establishing a new variational principle for relativistic calculationsof electronic structures.In this paper, on the basis of Brillouin's theorem and a relativisticmulticonfiguration Hartree-Fock (RMCHF) expansion in the{u+j, u-j; j=1,2,...,m} basis, we develop equations to annihilatethe coefficients of all single excitations to obtain very accurateRMCHF solutions.Moreover, after nullifying the coefficients of single excitations,the above inequality among energies becomes an equality,leading to a particular instance of an exact decoupling ofpositive-energy and negative-energy orbitals, irrespective of anyad hoc choice of potentials, hence rigorously justifying, forthe first time, the absence of explicit projection operators in allcurrent relativistic work where one-electron Dirac Hamiltoniansare involved.We present, also for the first time, relativistic Hartree-Fockapproximations for the ground states of He through Ar, which areaccurate to six decimals in a.u., and which converge to thenonrelativistic results when the speed of light c -> infinity.This accuracy was obtained by means of compact Slater-type orbitalexpansions through a direct translation of nonrelativistic Hartree-Fockwithout need to reoptimize nonlinear parameters. Our SCFequations are also valid for any open shells and for anyexcited states within a given symmetry, as exemplified withapplications to odd-parity, J = 1/2, 1s22s22p2np statesof neutral nitrogen. PACS Nos.: 31.10+z, 11.80Fv, 31.20Tz, 31.30Jv

Relativistic self-consistent-field atomic calculationsusing a generalization of Brillouin's theorem

When the one-body part of the relativistic Hamiltonian M is a sum of one-electron Dirac Hamiltonians, relativistic configuration interaction (CI) calculations are carried out on an ad hoc basis of positive-energy orbitals, t (=Ac2cc6, and more recently, with the full bases of positive-energy and negative-energy orbitals, t c (=Ac2cc6. The respective eigenproblems, + & =. & , &=1,2,..., E6 ,a nd+& =. & ; &=1,2,...,E26 are related through . $ . establishing a new variational principle for relativistic calculations of electronic structures. In this paper, on the basis of Brillouin's theorem and a relativistic multiconfiguration Hartree-Fock (RMCHF) expansion in the t c (=Ac2cc6 basis, we develop equations to annihilate the coefficients of all single excitations to obtain very accurate RMCHF solutions. Moreover, after nullifying the coefficients of single excitations, the above inequality among energies becomes an equality, leading to a particular instance of an exact decoupling of positive-energy and negative-energy orbitals, irrespective of any ad hoc choice of potentials, hence rigorously justifying, for the first time, the absence of explicit projection operators in all current relativistic work where one-electron Dirac Hamiltonians are involved. We present, also for the first time, relativistic Hartree-Fock approximations for the ground states of He through Ar, which are accurate to six decimals in a.u., and which converge to the nonrelativistic results when the speed of light S < . This accuracy was obtained by means of compact Slater-type orbital expansions through a direct translation of nonrelativistic Hartree-Fock without need to reoptimize nonlinear parameters. Our SCF equations are also valid for any open shells and for any excited states within a given symmetry, as exemplified with applications to odd-parity, a 'A *2, Ar 2r 2R ?R states of neutral nitrogen.

Wavelengths of neon-like 3p → 3s X-ray laser transitions

This paper presents the wavelengths of the neon-like 3p → 3s laser lines which have been observed in both lasing and nonlasing plasmas and compares the experimental wavelengths with relativistic multi-configuration Hartree-Fock calculations in order to estimate the wavelengths for these lines in all neon-like ions between S6+ and Xe44+. The seven 3p → 3s transitions which have been observed to lase in some neon-like ions are considered in this work.

Energies of nickel-like 4d to 4p laser lines

Relativistic multi-configuration Hartree-Fock calculations have been carried out for the energies of the nickel-like 4d to 4p X-ray lines which are potential lasing lines. Measurements of a set of these transition energies have also been made. Predicted wavelengths, covering the range of atomic numbers from Z = 46-92, have been derived by adjusting the ab initio energies by experimentally derived empirical constants.

Relativistic CI calculations for the ns2 1S0-nsnp 3P1, 1P1 transitions in the cadmium and mercury isoelectronic sequences

The relativistic configuration interaction approach based on numerical wavefunctions computed with a single-configuration relativistic Hartree-Fock method is employed to calculate ionisation and excitation energies as well as oscillator strengths for the ns2 1S0-nsnp 3P1, 1P1 transitions in cadmium and mercury isoelectronic sequences. The core polarisation model is used to account for valence-core correlation influence on both wavefunctions and total energies. The results are compared with previous relativistic multiconfiguration Hartree-Fock and other theoretical data as well as with available experimental values. It is demonstrated that the proposed relativistic CI approach yields accurate and reliable data at a far smaller computational expense than required for similar scale multiconfiguration calculations. It also permits us to avoid numerous convergence problems common for the multiconfiguration approach.

Comparison of relativistic CI and MCRHF calculations of oscillator strengths and excitation energies for the ns21S0-nsnp3P1,1P1transitions in neutral cadmium and mercury

The oscillator strengths and excitation energies for the ns21S0-nsnp 3P1, 1P1 transitions in neutral cadmium and mercury calculated in the configuration interaction (CI) approach based on numerical relativistic SCF wavefunctions are compared with the results of a multiconfiguration relativistic Hartree-Fock (MCRHF) scheme, which employs the same set of configurations. It is found that with careful choice of the method used to generate the valence orbitals, the relativistic configuration interaction treatment yields results comparable with those of the MCRHF approach. The influence on oscillator strengths and excitation energies of the additional nd2 and npnd configurations, which could not be included in MCRHF calculations because of difficulties with the convergence of the SCF process, is also studied and is found to be very small.

Cascade-corrected lifetime measurements for singly and doubly ionized indium

Lifetime measurements obtained by the beam-foil method are given for 13 levels in In II and 12 levels in In III. Particular attention has been paid to cascade correction with the application of a new arbitrarily normalized decay curves (ANDC) program. The results are compared with theory, and good agreement is found with recent multiconfiguration relativistic Hartree–Fock (MCRHF) calculations for the In II resonance transition. The results for 2P and 2D levels in In III and 1D levels in In II indicate a need for further calculations.

Electron collisional excitation in F-like selenium.

Electron collisional excitation of the low-lying 1${s}^{2}$2${s}^{2}$2${p}^{5}$ and 1${s}^{2}$2s2${p}^{6}$ states of F-like selenium to the singly excited M-shell states is studied using a relativistic distorted-wave model and multiconfigurational relativistic Hartree-Fock bound states. Results are presented for all 2-3 transitions from the low-lying 2${s}^{2}$2${p}^{5}$ $^{2}\mathrm{P}_{3/2}$ and $^{2}\mathrm{P}_{1/2}$ levels, and also the 2s2${p}^{6}$ $^{2}\mathrm{S}_{1/2}$ level. We find a number of strong dipole-allowed 2p-3d cross sections with peak values near threshold in excess of ${10}^{\mathrm{\ensuremath{-}}20}$ ${\mathrm{cm}}^{2}$, and derive Gaunt factors which are in good agreement with values used in the literature (0.15--0.20) for most strong transitions.Very strong monopole 2p-3p excitation cross sections have been important in soft-x-ray laser theory, and are found to be as strong as the largest dipole-allowed cross sections for F-like selenium. Theoretical output powers for the strong lines of the 2p-3s, 2p-3d, and 2s-3p transition arrays are computed and presented for plasma conditions of ${N}_{e}$=3\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and ${T}_{e}$=1.0 keV. These results are compared in detail for proportionality against gf values for each array separately, as a test of how well line intensities might be judged from gf values in the absence of detailed theoretical intensity results. We find that for the 2p-3s and 2p-3d arrays, the intensities are in fair agreement with gf values within the array, while the agreement is much poorer in the case of the 2s-3p array. The two weaker arrays 2p-3s and 2s-3p are found to radiate more per unit gf than the 2p-3d transition array, in agreement with earlier observations in the Ne-like sequence. Theoretical line positions are tabulated for all strong 2-3 lines, and found to be in good agreement with experimental results for most strong transitions. Gains on the 3-3 transitions in between 2 and 4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are predicted for four lines under the plasma conditions quoted. Such conditions are similar to those of the recent extreme-uv laser experiments at the Lawrence Livermore National Laboratory, yet no F-like 3-3 amplification has yet been observed for F-like transitions. The discrepancy is currently a mystery.

Allowed and Forbidden n = 2?2 Transitions of the Elements Kr and Mo

Relativistic intermediate-coupling wavefunctions are used to evaluate transition energies, line strengths and transition probabilities for all allowed and forbidden n = 2-2 transitions for krypton and molybdenum beryllium-like ions. Our results are in very good agreement with those calculated using the relativistic multi-configuration Hartree-Fock approximation. These calculations were carried out under the same physical assumption that the dominant correlation effect is the n = 2 intra-shell correlation. We also discuss the importance of relativistic effects on the radial functions, the relativistic intermediate-coupling scheme in the variational process, the importance of radiative corrections for transition energies between states with different occupation of the 2s shell, and the relative importance of intra- versus inter-shell correlation effects.

Oscillator strengths of the2sS122−2pP12,32o2transitions in Fe xxiv and the2s2S01−2s2pP1o3transition in Fe xxiii

We have used the beam-foil technique to measure the mean lives of the upper levels of: (i) the 2s /sup 2/S/sub 1/2/ - 2p /sup 2/P/sup o//sub 1/2,3/2/ resonance transitions (at 255 and 192 A) in lithiumlike Fe XXIV and (ii) the 2s/sup 2/ /sup 1/S/sub 0/ - 2s2p /sup 3/P/sup o//sub 1/ intersystem transition (at 264 A) in berylliumlike Fe XXIII. The measured mean lives are tau (2p /sup 2/P/sup o//sub 1/2/) = 0.55 +- 0.02, tau (2p /sup 2/P/sup o//sub 3/2/) = 0.235 +- 0.01, and tau (2s2p /sup 3/P/sup o//sub 1/) = 13 +- 4 ns. Oscillator strengths derived from the Fe XXIV results are in good agreement with recent relativistic multiconfiguration Hartree-Fock (MCHF) ''length'' gauge calculations; the Fe XXIII result is not in agreement with these MCHF calculations, but appears to be in agreement with recent intermediate coupling calculations.

Fine structure in the 1s2p24P and 1s2s2p4P0states of Li-like

The fine structure intervals in the 1s2p2 4P and 1s2s2p 4P0 states of Li-like ions (Z<or=26) have been calculated from relativistic multiconfiguration Hartree-Fock wavefunctions. It is found that the Breit interaction plays a crucial role in attaining a good agreement with recent experimental data on C3+, N4+ and O5+ by Livingston and Berry (1978).

Excitation energies and line strengths in the Mg isoelectronic sequence

Excitation energies and line strengths for the low-lying states of ions in the Mg isoelectronic sequence are studied using relativistic multiconfiguration Hartree-Fock techniques. Line strengths for all possible electric dipole transitions between these low-lying states are calculated in both the length gauge and in the velocity gauge along the sequence from Mg to ${\mathrm{U}}^{+80}$, and the results show good agreement between these two forms of line strength for all cases considered. At low $Z$, the results of the present work are in good agreement with other recent theoretical calculations. The results of this work are expected to give accurate excitation energies and line strengths at high $Z$ as well since relativistic effects are treated nonperturbatively.