Multiconfiguration Dirac-Fock Method Research Articles

Energies and electric dipole transitions for triply ionized Kr, Xe and Rn

Energies and transition parameters such as wavelengths, transition probabilities (rates) and oscillator strengths for the electric dipole (E1) transitions have been reported for triply ionized krypton (Z = 36), xenon (Z = 54) and radon (Z = 86) using the general-purpose relativistic atomic structure package based on a fully relativistic multiconfiguration Dirac–Fock method. The Breit interactions for the relativistic effects, quantum electrodynamical contributions and correlation effects have been included in calculations. Obtained results have been compared with available theoretical and experimental values in the literature. Most of results, in particular for Rn IV, have been presented firstly.

Analysis of discrepancy in previously published excitation energies of Ne-like ions from two independent codes and atomic data of Rb XXVIII and Ba XLVII

Fine structure energies and radiative data namely, transition wavelength, transitions rates, oscillator strength and line strength have been presented for lowest 75 levels of highly ionized Ne-like Rb27+ (Rb XXVIII) and Ne-like Ba46+ (Ba XLVII) by using Multi-Configuration Dirac-Fock (MCDF) method. Our presented transition X-ray wavelengths of Ne-like Rb match well with Ne-like Rb experimentally determined laser wavelengths from different laser techniques. We have analyzed inconsistencies and uncertainties in previous Ne-like ions results by the evaluation of results from two independent codes general purpose relativistic atomic structure package (GRASP) and flexible atomic code (FAC). Our excitation energies for Rb XXVIII and Ba XLVII match well with NIST and other available results. We demonstrate that inclusion of configuration interaction (CI) is crucial to attain the accuracy in atomic data calculations. The present results are complete, extensive and in good agreement with other results and believe that presented results will be effective and helpful in detection of other X-ray spectral lines of Ne-like Rb laser from different sources.

KLL dielectronic recombination of hydrogenlike carbon ion in Debye plasmas

The KLL dielectronic recombination (DR) process of C5+ ion embedded in Debye plasmas is investigated using the multiconfiguration Dirac-Fock method with the Debye-Hückel model potential. The resonance energies, radiative and Auger rates as well as DR cross sections are obtained for a large range of Debye screening parameters to explore the influences of the plasma screening on the KLL DR process of C5+ ion. It is found that the total radiative rates and Auger rates of the intermediate states both decrease monotonically with increasing the plasma screening, except the Auger rate for the transition 2p2 1S → 1s that changes nonmonotonically due to such screening imposed on the interaction between the configurations 1s and 2s in C5+ ion. Moreover, for the KLL DR process, blueshift and redshift phenomena are observed for the resonance energies, which originates from the dynamic variations of the energy levels of C4+ and C5+ ions in the Debye plasma. The magnitudes of the DR cross section decrease slightly when the Debye-screening effects are not so strong.

Multiconfiguration Dirac–Fock calculations of Zn K‐shell radiative and nonradiative transitions

Zinc K‐shell radiative and radiationless transition rates are calculated using the multiconfiguration Dirac–Fock method. Correlation up to the 4p orbital is included in almost all transition rate calculations. Calculated radiative transition rates and transition probabilities are compared with Scofield's Dirac–Hartree–Slater and Dirac–Hartree–Fock calculations, presenting good agreement with the later. Radiative transition intensity ratios involving the strongest lines are compared with theoretical, experimental, and empirical‐fit values. Most ratios are in close agreement with the empirical‐fit values from NIST's Fundamental Parameters database. Calculated radiationless transition rates and ratios are compared with Chen et al.'s Dirac–Fock values and Safronova et al.'s Dirac–Fock values. The K‐LL transition rates are overall lower than Chen et al.'s values, whereas the K‐LX and K‐XY transition rates are overall higher. Calculated K‐LX/K‐LL and K‐XY/K‐LL ratios are relatively close to the experimental values compared. Some calculated intensities relative to K‐L are in good agreement with the experimental values, whereas others present worse agreement. The calculated fluorescence yield is higher than all theoretical, experimental, and empirical‐fitted values compared, probably because the total radiationless transition rate value calculated in the present work is relatively low.

Calculation of the energies and oscillator strengths of Cl[formula omitted] in hot dense plasmas

The high-resolution measurements of Beiersdorfer et al. [Phys. Rev. A 100, 012511 (2019)] for the shifts of the 1s3p1P1 → 1s2 1S0 He-β transition of Cl15+ are in significant disagreement with a generalized analytical approach calculations of Li and Rosmej [Europhys. Lett. 99, 33001 (2012)]. The multi-configuration Dirac–Fock method incorporating the average-atom ion-sphere model is applied to the problem. Our results are in good agreement with the experimental data across the full range of electron density measured. Oscillator strengths are also given. Systematic trends are observed for the properties under study regarding to increased temperature and electron density.

Influence of plasma screening on the energies and transition properties of the Al9+ ion using Debye and ion-sphere models

Investigations on the energies and radiative properties of a highly charged ion embedded in plasma in the weak- and strong-coupling regimes are made, taking the Al9+ ion as an example. The Debye and ion-sphere (IS) potentials are adopted to describe the plasma screening effects, respectively. The multiconfiguration Dirac-Fock (MCDF) method is employed to describe the relativistic and electronic correlation effects in the above atomic system. The screening effects on the ionization potential (IP), transition energies, and radiative rates are estimated. Results obtained are compared with the available results in the literature. Comparisons between the Debye and IS models results are also carried out considering similar plasma conditions. The present data are useful for diagnostics of astrophysical and laboratory plasmas.

Extended calculations for energies and EUV transition data of W LIII

Energy spectra of the 3d4, 3d34s, 3d34p, and 3d34d configurations of W LIII are calculated using the ab initio multi-configuration Dirac-Fock method. The correlations within the n = 9 complex, n being the principal quantum number of the outermost electron are accounted for in a systematic way and the Breit interaction and quantum electrodynamics effect are evaluated. Wavelengths, oscillator strengths, electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole emission transition rates regarding these levels are obtained. The Flexible Atomic Code (FAC) calculations are further performed to support these data. Results are compared with other available theory reported in the literature as well as the recommended experimental data listed in the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST) online database. Satisfactory agreement is found between them. In light of these findings, the present complete and consistent results can aid line identifications in extreme ultraviolet (EUV) spectra and should be beneficial in fusion plasma research.

Relativistic atomic structure calculations and study of plasma parameters for Na-like Se XXIV

Extensive calculations of energy levels and radiative data such as transition wavelengths, radiative rates, oscillator strengths, and line strengths for electric dipole (E1) transitions have been performed for Se XXIV using the multiconfiguration Dirac–Fock method. For other types of transitions, namely, magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2), only the radiative rates (A) are listed. The importance and effect of valence-valence and core-valence correlations on the excitation energies have been studied. For additional accuracy assessments, analogous calculations have been carried out by employing the flexible atomic code and configuration interaction technique. Comparisons are made with the available experimental and theoretical data in the literature. Close agreement has been found ensuring the accuracy and reliability of our results. The effect of plasma temperature on the line intensity ratio, electron density, plasma frequency, and skin depth has been analyzed for hot dense plasma (HDP) in local thermodynamic equilibrium. The present work might be beneficial in the modeling and characterization of HDP.

Study of relativistic excitation energies and transition data for EUV and SXR spectral lines in Ge XXIX and Kr XXXIII of fusion interest

Based on relativistic wavefunctions from multi-configurational Dirac–Fock method, a comprehensive theoretical study of atomic characteristics of energy levels, wavelengths, lifetimes, electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole radiative rates is performed for the lowest 98 levels of the 2s2, 2p2, 2s3s, 2s3d, 2p3p, 2s4s, 2s4d, 2p4p, 2p4f, 2s2p, 2s3p, 2p3s, 2p3d, 2s4p, 2s4f, 2p4s, and 2p4d configurations of Ge XXIX and Kr XXXIII. The correlations within the n=9 complex, n being the principal quantum number of the outermost electron are accounted for in a systematic way and the Breit interactions and quantum electrodynamics effects are estimated. Similar data are also determined using the many-body perturbation theory. The accuracy of our results is determined through extensive comparisons with the available data from the Atomic Spectra Database of the National Institute of Standards and Technology and with published theoretical values. Our computed wavelengths are almost of spectroscopic accuracy, aiding line identification in extreme ultraviolet (EUV) and soft X-ray (SXR) spectra. The present complete set of data are very useful for modeling and diagnosing fusion plasmas.

Analysis of configuration interaction and convergence with energy levels and radiative data in W XXXIX

Fine structure energies and radiative data namely, transition wavelength, transitions rates, oscillator strength and line strength have been presented for lowest 123 levels of Kr-like W (WXXXIX) by using Multi-Configuration Dirac-Fock (MCDF) method. We have systematically analysed configuration interaction (CI) and convergence in radiative data and Dirac-Coulomb as well as Breit and Quantum electrodynamics (QED) effects of excitation energies. We demonstrate that inclusion of CI and convergence in excitation energies are crucial to attain the accuracy in atomic data. We have also discussed the evaluation of results from two independent codes GRASP and FAC based on MCDF and Distorted Wave (DW). We show that magnetic multipole transitions (M1, M2) are dominant in the contribution of lifetime of 4 s2(1S0) 4p5(2P1) 4f1(2F1)3D1 and 4 s1(2S1) 4p5(2P1) 4d2(3F2)3D2o. The present results are complete, extensive and in good agreement with other results.

Diagnosing the lightning plasma temperature based on the collisional-radiative model

Energy levels, transition probabilities, collision sections, and collision excitation rate coefficients of NII ion have been calculated using Flexible Atomic Code, which is based on the multiconfiguration Dirac–Fock method. The ratios of line intensity, I567.96 nm/I500.52 nm, where the 567.96 and 500.52 nm are two strong spectral lines from the core current channel of lightning, have been calculated by using the collisional-radiative model, in which the line intensity is proportional to the collision excitation rate coefficients from the ground state to the excited state and the transition probability from the high excited state to the low excited state. The temperatures of six lightning plasma channels were then obtained, and they are consistent with temperatures obtained by diagnosing the actual spectrum with the multispectral line method.

L-shell spectroscopy of neon and fluorine like copper ions from laser produced plasma

Ne, F, and O-like Rydberg resonance lines along with some of the inner shell satellite lines of Copper plasma, in the wavelength range of 7.9–9.5 Å, are experimentally observed using a thallium acid phthalate crystal spectrometer. The plasma is produced by the irradiation of a Cu target with a 15 J, 500 ps Nd: Glass laser with a focusable intensity up to 5 × 1014 W/cm2. The observed lines result from the transitions among 2p-nd, 2p-ns, and 2s-nd (n = 4–6) levels. Transition wavelengths, transition probabilities, and oscillator strengths of these lines are calculated using the Multi-Configuration Dirac-Fock method. In this computation, the contribution of relativistic corrections such as two-body Breit corrections and QED corrections due to vacuum polarization and self-energy has also been considered. FLYCHK simulations are used to analyze the distribution of the various charge states of the Copper ions and to find the temperature and density of plasma. Moreover, the effect of self-absorption of the plasma (opacity), as well as of suprathermal electrons on charge state distribution of ions, is also studied. The synthetic spectrum provides a best-match with the experimental spectrum at a laser intensity of 1.3 × 1014 W/cm2 for Tc = 150 eV, Th = 1000 eV, f = 0.008, and density 4.5 × 1020 cm−3.The temperature and density ranges are also calculated using a radiative hydrodynamic code. The calculated temperature and density range are in agreement with the experimentally determined values. The effect of the change in laser intensity on the L-shell spectrum of Cu is studied which indicates the switching between lower (Cu XX) and higher charge states (Cu XXI and Cu XXII) at higher laser intensities.

Spectroscopic study of EUV and SXR transitions of Cu XIX with plasma parameters

Extensive and elaborate theoretical computations of Cu XIX have been performed by employing multi-configuration Dirac-Fock (MCDF) method. We have presented energy levels and radiative data such as, transition wavelengths, radiative rates, oscillator strengths and line strengths for electric dipole (E1) transitions in Na-like Cu. For other types of transitions, namely magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2), only the A-values are listed. We have also discussed the importance and the effect of valence-valence (VV) and core-valence (CV) correlations on the excitation energies in graphical as well as in tabular form. The accuracies of the presented levels, wavelengths, transition rates and lifetimes are assessed by comparing them to available experimental and other theoretical results. Analogous calculations have been carried out by using Flexible Atomic Code (FAC) based on self-consistent Dirac-Fock-Slater iteration method. QED corrections due to vacuum polarization and self-energy effects, and Breit correction due to the exchange of virtual photons between two electrons are fully considered and their effects on the energy levels are studied graphically. The fine-structure energy levels have also been reported by using the Configuration Interaction (CIV3) technique. An intercomparison among three independent calculations helps us in assessing the credibility and integrity of our reported data. Additionally, we have shown the variation of the line intensity ratios and electron density with plasma temperature graphically for Cu XIX. We have also identified Extreme Ultraviolet (EUV) and Soft X-ray (SXR) transitions and believe that our reported results may be beneficial in space and laboratory plasma research.

Extended atomic structure calculations for energy levels and radiative data of Xe XLIII

We report an extensive and elaborate theoretical study of atomic data for Xe XLIII. We have calculated energies for the lowest 141 fin. structure levels by using Multi-Configuration Dirac Fock (MCDF) method. We have also considered Quantum Electrodynamics (QED) and Breit corrections in our calculations. We have presented the radiative data for electric dipole (E1) transitions among lowest 141 levels. We have made comparisons of our calculated excitation energies and EUV (Extreme Ultraviolet) transition wavelengths with the theoretically computed and experimentally observed energy levels and wavelengths at Electron Beam Ion Trap (EBIT) and a good agreement is achieved. We have also computed energy levels by performing similar relativistic distorted wave calculations using Flexible Atomic Code (FAC). Additionally, we have provided new atomic data for Xe XLIII which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and detection and investigation of EUV and Soft X-ray (SXR) spectral lines.

Atomic structure calculations, partition function, and thermodynamic parameters for W LXXII and Au LXXVII

In this work, we present a theoretical study of W LXXII (Li-like W71+) and Au LXXVII (Li-like Au76+) by employing a multi-configuration Dirac Fock method approach within the framework of the Dirac-Coulomb Hamiltonian including quantum electrodynamics and Breit corrections. We have presented energies of the lowest 42 fine structure energy levels and radiative data for electric dipole (E1) transitions within the lowest 42 levels. We have made comparisons with available energy levels compiled by NIST and achieved good agreement. We have also discussed discrepancies between our results and other theoretical results with possible reasons of discrepancy. Due to inadequate data in the literature for higher excited states, analogous relativistic distorted wave calculations have also been performed using the flexible atomic code to assess the reliability and accuracy of our results. Furthermore, we have calculated the partition function and thermodynamic properties by the fine structure approach. The variation of the partition function, internal energy, and specific heat with temperature is also discussed. We believe that our presented work and future comparisons with experimental observations will be beneficial in fusion plasma.

Spectroscopic study of EUV and SXR transitions of Cs XXV

We report an extensive and elaborate theoretical study of atomic data for Cs XXV by using multi-configuration Dirac–Fock method and calculated energy levels for the lowest 110 fine structure levels. We have presented the radiative data for electric and magnetic dipole (E1, M1) and quadrupole (E2, M2) transitions among lowest 110 levels. We have made comparisons of our calculated excitation energies with theoretically calculated and experimentally observed energy levels. We have studied the effect of correlation by introducing more configurations in our calculations. We have also computed energy levels by performing similar relativistic distorted wave calculations using Flexible Atomic Code. Additionally, we have also provided new atomic data for Cs XXV and identified extreme ultraviolet and soft X-ray spectral lines with gA spectra for E1 and M2 transitions, which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and applications.

Relativistic effects on the energy levels and radiative properties of He-like ions immersed in Debye plasmas

Systematic investigations are performed for the energy levels and radiative properties for selected He-like C4+, Ne8+, Ar16+, and Kr34+ ions embedded in weakly coupled plasmas. For the conditions in which the Coulomb coupling parameter is small, the standard Debye model is adopted to describe the plasma screening effects. Within the relativistic framework, the modified version of the Flexible Atomic Code computations is carried out by considering a Debye-Hückel potential, in which the plasma screening is taken into account for both the electron-nucleus and electron-electron (e-e) interactions. An independent calculation for various Debye lengths is also presented using the multiconfiguration Dirac-Fock method for comparison purposes. For the nonrelativistic treatment, the analytical solution of the Schrödinger equation with the Debye screened potential is proposed. The variation method is developed with Slater wave function as a trial wave function that contains the variational parameters. An exact analytical expression of relativistic corrections such as the mass-velocity correction, the one/two-body Darwin correction, the spin-spin contact interaction correction, and the orbit-orbit interaction correction is derived. Differences among our three kinds of calculated energy levels and transition properties are analyzed in terms of the nuclear charge and/or the Debye length. Systematic trend is observed for all the properties under study with respect to increased screening. The influence of relativistic effects is also investigated in detail and found to play an important role in these systems. Our results are compared with available results from other theoretical calculations and the experimental values in the literature, and a good agreement is achieved. This work should be useful for astrophysical applications where such plasma environments exist.

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.

A structure calculation for hydrogen like nobelium

The hydrogen like ion is the simplest structure of an atom, so the studying on it gives a change to test of methods using for determinating of atomic structures. It is also an occasion the studying on hydrogen like ions to understand atomic structure. For this reason, it is performed a study for hydrogen like nobelium (No101+, Z=102). The calculating level structure of No101+ have been used both multiconfiguration Hartree-Fock and multiconfiguration Dirac-Fock method. The calculations have contained some relativistic corrections and quantum electrodynamic effects. There are very few theoretical works in available literature and no experimental one for No101+. The calculated results have been interpreted in comparison with other theoretical results.

Single and double Auger decay of 4f-ionized mercury including cascade and direct processes**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant Nos. 11774344 and 11474033), and the Joint Foundation of the National Natural Science Foundation and the China Academy of Engineering Physics (Grant No. U1330117).

Single (SA) and double (DA) Auger decay including cascade and direct processes are investigated for Hg 4f−1 with multiconfiguration Dirac–Fock method and two-step approaches, i.e., knockout and shakeoff mechanisms. Due to the computational effort, only the major transitions are considered to describe the SA and DA decays for the Hg+ ions with complex electronic configurations. In order to estimate the Auger transition energies and amplitudes, the reference configuration sets producing the configuration state functions are carefully chosen for balancing electron correlations among the successive singly, doubly and triply ionized mercury. The Auger rates and electron spectra, DA probabilities as well as the populations of the final Hg3+ states are obtained. Our results well explain the recent experimental data about the 4f hole states of Hg [Palaudoux J et al., Phys. Rev. A 91 012513 (2015)], and could provide guidance for further studies on complex atoms. Particularly for the DA decay, the contributions of the direct processes, which are neglected in their calculations, are found to be important, accounting for as high as about 38% and 34% of the total DA decays for the and , respectively.