Relativistic Configuration Interaction Method Research Articles

Visible Light-Induced Homolytic Cleavage of Perfluoroalkyl Iodides Mediated by Phosphines.

In an effort to explain the experimentally observed variation of the photocatalytic activity of BuP, BuP and (MeO)P in the blue-light regime [Helmecke et al., Org. Lett. 21 (2019) 7823], we have explored the absorption characteristics of several phosphine– and phosphite–ICF adducts by means of relativistic density functional theory and multireference configuration interaction methods. Based on the results of these computational and complementary experimental studies, we offer an explanation for the broad tailing of the absorption of BuP-ICF and (MeO)P-ICF into the visible-light region. Larger coordinate displacements of the ground and excited singlet potential energy wells in BuP-ICF, in particular with regard to the P–I–C bending angle, reduce the Franck–Condon factors and thus the absorption probability compared to BuP-ICF. Spectroscopic and computational evaluation of conformationally flexible and locked phosphites suggests that the reactivity of (MeO)P may be the result of oxygen lone-pair participation and concomitant broadening of absorption. The proposed mechanism for the phosphine-catalyzed homolytic C–I cleavage of perfluorobutane iodide involves S1 ← S0 absorption of the adduct followed by intersystem crossing to the photochemically active T state.

Calculations of transition rates in erbium-like ions Lu IV, Hf V and Ta VI using the Ab initio MCDHF-RCI and semi-empirical HFR methods

In the present paper, the radiative properties of three ions belonging to the erbium isoelectronic sequence, i.e. Lu IV, Hf V and Ta IV, are reported and the effect of configuration interaction on these properties are taken into account for the first time to our knowledge. These heavy elements with Z=71–73 are located near to tungsten (Z=74) in the Periodic Table and are of potential interest in controlled thermonuclear fusion. Indeed, they could be used in plasma-facing materials such as the divertors in tokamaks or/and could be generated by neutron-induced transmutations of divertor’s materials. In this work, two independent theoretical atomic structure computational approaches have been considered, i.e. the semi-empirical Hartree–Fock with relativistic corrections method (HFR) and the ab initio multiconfiguration Dirac–Hartree–Fock with subsequent relativistic configuration interaction method (MCDHF-RCI). The transition probabilities and the oscillator strengths have been calculated for 593, 820 and 1101 E1 transitions in Lu IV, Hf V and Ta VI respectively spanning the spectral range from UV to IR. Finally, this study also underlines the importance of core-valence correlations in these heavy atomic ions.

Enhancement of electron–ion recombination rates at low energy range in the heavy ion storage ring CSRm**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300) and the National Natural Science Foundation of China (Grant Nos. U1932207, 11904371, and U1732133).

Recombination of Ar14+, Ar15+, Ca16+, and Ni19+ ions with electrons has been investigated at low energy range based on the merged-beam method at the main cooler storage ring CSRm in the Institute of Modern Physics, Lanzhou, China. For each ion, the absolute recombination rate coefficients have been measured with electron–ion collision energies from 0 meV to 1000 meV which include the radiative recombination (RR) and also dielectronic recombination (DR) processes. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semi-classical Bethe and Salpeter formula for hydrogenic ions. DR cross sections were calculated by a relativistic configuration interaction method using the flexible atomic code (FAC) and AUTOSTRUCTURE code in this energy range. The calculated RR + DR rate coefficients show a good agreement with the measured value at the collision energy above 100 meV. However, large discrepancies have been found at low energy range especially below 10 meV, and the experimental results show a strong enhancement relative to the theoretical RR rate coefficients. For the electron–ion collision energy below 1 meV, it was found that the experimentally observed recombination rates are higher than the theoretically predicted and fitted rates by a factor of 1.5 to 3.9. The strong dependence of RR rate coefficient enhancement on the charge state of the ions has been found with the scaling rule of q3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.

Theoretical study of the dielectronic recombination process of Mg-like W62+ ions

SynopsisThe dielectronic recombination of Mg-like W62+ (3s2) ions was studied using the flexible atomic code based on the relativistic configuration interaction method with considering Breit and QED corrections. Theoretical results are compared with the experimental results from electron beam ion trap, good consistency is obtained.

Theoretical investigation of electron-ion recombination process of Fe14+ ion

SynopsisThe Δn=1 dielectronic, trielectronic, and quadruelectronic recombinations of Fe14+ ion are systematically studied using the flexible atomic code based on the relativistic configuration interaction method. The theoretical rate coefficients are identified and compared with the experimental measurements at heavy-ion storage ring (TSR), good agreement is obtained.

Combined MCDHF-CI and MBPT calculations for n=4 to n=3 x-ray transitions in Ni-like tungsten

SynopsisThe 4d → 3p, 4p → 3s, and 4f → 3p x-ray transitions in Ni-like tungsten ions have been studied theoretically. The Multiconfiguration Dirac–Hartree–Fock method and the large-scale relativistic Configuration Interaction and Many Body Perturbation Theory methods have been employed in order to take into account electron correlation effects on the lines wavelengths.

Effect of Dense Plasma Environment on the Spectroscopic Properties of He-like Ca18+ Ion

Plasma shielding effects on the energy levels and radiative properties of He-like Ca\(^{18+}\) ion under dense plasma conditions have been studied. For this purpose, the multiconfiguration Dirac-Fock method has been implemented by incorporating the ion sphere model potential as a modified interaction potential between the electron and the nucleus. To check the authenticity of our results, independent calculations have been performed using the modified relativistic configuration interaction method. It is observed that the transition energies associated with \(\Delta n = 0\) transitions are blue shifted, whereas red shifted for \(\Delta n \neq 0\) transitions. The variation in transition probabilities and weighted oscillator strengths with plasma densities has also been analyzed. The present results should be beneficial in the plasma modeling and fusion plasma research applications.

Parameters of Isotope Shifts for 2s2p 3,1P1 → 2s2 1S0 Transitions in Heavy Be-Like Ions**Supported by the National Natural Science Foundation of China under Grant Nos 11874090, 11604385, 91536106 and 11204374, and the Research Project of National University of Defense Technology under Grant No ZK17-03-11.

The field shift and mass shift parameters of the 2s2p 3,1P1 → 2s2 1S0 transitions in Be-like ions (70 ≤ Z ≤ 92) are calculated using the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods with the inclusion of the Breit interaction and the leading QED corrections. We find that the mass shift parameters of these two transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects. A minimum value exists for the specific mass shift parameters around Z = 80, especially for the 2s2p 3P1 → 2s2 1S0 transition. In addition, the field shifts and mass shifts of these two transitions are estimated using an empirical formula, and their contributions are compared along the isoelectronic sequence.

Polarization of fluorescence radiation following electron impact excitation of ions immersed in strongly coupled plasmas

An investigation on the electron impact excitation and subsequent radiative decay process of He-like Fe24+ ions immersed in strongly coupled plasmas is made, using the 1s2p P3,11 → 1s2 S10 characteristic lines as an example. The shielded nuclear potential of the uniform electron gas model (UEGM) type experienced by the electron is parameterized by the ion-sphere radius. For the target structure, accuracies of wave functions are justified by evaluating the energies of the relevant states. To serve as an independent check of the results, self-consistent calculations are carried out using the multiconfiguration Dirac-Fock relativistic configuration interaction method incorporating the same potential. For the impact excitation process, the UEGM potential is also employed to screen the projectile electron from the nucleus and target electrons. A distorted-wave method in the framework of the relativistic theory is developed to include the effect of plasma background, in which the continuum wave function of the projectile electron is evaluated by solving numerically the modified Dirac equations. The plasma effects on the total excitation cross section, magnetic sublevel cross section, and linear polarization of fluorescence radiation are investigated. The comparison with the available theoretical and experimental results is satisfactory.

Dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr lattice clock

The progress in optical clock with uncertainty at a level of $10^{-18}$ requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Current theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the magic wavelength for the Sr clock differ substantially. We develop a combined approach of the Dirac-Fock plus core polarization (DFCP) and relativistic configuration interaction (RCI) methods to calculate dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr atom. Our differential dynamic hyperpolarizability at the magic wavelength is $-2.09(43)\times10^{7}$ a.u., which is consistent with the existing theoretical and experimental results. Our differential multipolar polarizability is $2.68(94)\times 10^{-5}$ a.u., which validates independently the theoretical work of Porsev {\em et al.} [Phys. Rev. Lett. 120, 063204 (2018)], but different from recent measurement of Ushijima {\em et al.} [Phys. Rev. Lett. 121, 263202 (2018)].

Theoretical Energy Levels of 1sns and 1snp States of Helium-Like Ions

Energy levels of the 1sns and 1snp states of ions along the helium isoelectronic sequence from carbon to uranium are calculated, with n = 3–7. The computation is performed within the relativistic configuration-interaction method, including the relativistic nuclear recoil effect, the leading quantum electrodynamics effects, and the frequency dependence of the Breit interaction. All theoretical energies are supplied with uncertainty estimates.

Radiative de-excitations of the 1s2s3s configuration of Li-like ions

The fully relativistic configuration interaction method is used to study the one-electron one-photon (OEOP) and two-electron one-photon (TEOP) transitions between the 1s2s3s and the respective 1s2s2p and 1s2np (n = 2–4 ) groups of Li-like ions with 12 ≤ Z ≤ 54. The transition properties are calculated using multi-configuration Dirac–Fock wavefunctions in the active space approximation taking into account the correlated state functions that have non-negligible contributions to the mixing coefficients. The drastic variations in the level lifetimes due especially to 1s2s3s-1s2np (n = 2, 3) transitions are analyzed in detail. The OEOP transition energies are far less than those of TEOP transitions and have been taken up in this work mainly to investigate the most probable radiative decay channel and also to understand the interplay between electron–electron correlation and the low-frequency limit transverse photon interaction on the mixing coefficients of J = 3/2 states of 1s2s2p around Z = 21. The present results are compared with other available data.

Dielectronic recombination rate coefficients of fluorine-like nickel

Electron-ion recombination rate coefficients for fluorine-like nickel ions have been measured by employing the merged-beam technique at the cooler storage ring CSRm at the Institute of Modern Physics in Lanzhou, China. The measured spectrum covers the energy range of 0–160 eV, including all the dielectronic recombination (DR) resonances associated with ΔN = 0 core excitations. The DR cross sections in this energy range were calculated by a relativistic configuration interaction method using the flexible atomic code (FAC). Radiative recombination (RR) cross sections were obtained from a modified version of the semi-classical Bethe & Salpeter (1957, Quantum Mechanics of One- and Two-Electron 56 Systems (Springer)) formula for hydrogenic ions. The comparison between the measurement and the calculation shows that the present theoretical model still needs to be improved at low collision energies. Temperature dependent plasma recombination rate coefficients were derived from the measured DR rate coefficients in the temperature range of 103–108 K and compared with the presently calculated result as well as previous available data in the literature. The experimentally derived data agree well with the theoretical calculations for temperatures where Ni19+ ions form in collisionally ionized plasmas. At lower temperatures typical for photo-ionized plasmas, discrepancies are found beyond the experimental uncertainty, which can be attributed to the disagreement between the measurement and the calculation of the low-lying DR resonances. The present experimental result benchmarks the plasma DR rate coefficients, in particular for temperatures below 105 K where the ΔN = 0 DR resonances dominate.

Observation of indirect ionization of W7+ in an electron-beam ion-trap plasma

In this work, visible and extreme ultraviolet spectra of W7+ are measured using the high-temperature superconducting electron-beam ion trap (EBIT) at the Shanghai EBIT Laboratory under extremely low-energy conditions (lower than the nominal electron-beam energy of 130 eV). The relevant atomic structure is calculated using the flexible atomic code package based on the relativistic configuration interaction method. The GRASP2K code, in the framework of the multiconfiguration Dirac-Hartree-Fock method, is employed as well for calculating the wavelength of the M1 transition in the ground configuration of W7+. A line from the W7+ ions is observed at a little higher electron-beam energy than the ionization potential for W4+, making this line appear to be from W5+. A hypothesis for the charge-state evolution of W7+ is proposed based on our experimental and theoretical results; that is, the occurrence of W7+ ions results from indirect ionization caused by stepwise excitation between some metastable states of lower-charge-state W ions, at the nominal electron-beam energy of 59 eV.

Relativistic calculations of the ground and inner- L -shell excited energy levels of berylliumlike ions

Large-scale relativistic configuration-interaction method combined with many-body perturbation theory is consistently applied to calculations of the energy levels of the ground and inner-L-shell excited states of berylliumlike ions in the range $10 \leq Z \leq 92$. The quantum electrodynamics, nuclear recoil, and frequency-dependent Breit corrections are taken into account. The obtained results are supplemented with the systematical estimation of the uncertainties.

Theoretical investigation of energy levels and transition data for S II, Cl III, Ar IV

Aims. The aim of this work is to present accurate and extensive results of energy spectra and transition data for the S II, Cl III, and Ar IV ions. These data are useful for understanding and probing physical processes and conditions in various types of astrophysical plasmas.Methods. The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, are used in the present work. In the RCI calculations the transverse-photon (Breit) interaction, the vacuum polarization, and the self-energy corrections are included.Results. Energy spectra are presented comprising the 134, 87, and 103 lowest states in S II, Cl III, and Ar IV, respectively. Energy levels are in very good agreement with NIST database recommended values and associated with smaller uncertainties than energies from other theoretical computations. Electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transition data are computed between the above states together with the corresponding lifetimes. Based on internal validation, transition rates for the majority of the stronger transitions are estimated to have uncertainties of less than 3%.

Extended Calculations of Energy Levels and Transition Rates of Nd ii-iv Ions for Application to Neutron Star Mergers

Abstract The coalescence of a binary neutron star gives rise to electromagnetic emission, known as a kilonova, that is powered by radioactive decays of r-process nuclei. Observations of a kilonova associated with GW170817 provide a unique opportunity to study heavy element synthesis in the universe. However, the atomic data of r-process elements are not yet complete enough to decipher the light curves and spectral features of kilonovae. In this paper, we perform extended atomic calculations of neodymium (Nd, Z = 60) to study the impact of the accuracy in atomic calculations on astrophysical opacities. By employing multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods, we calculate the energy levels and transition data of electric dipole transitions for Nd ii, Nd iii, and Nd iv ions. Compared with previous calculations, our new results provide better agreement with the experimental data. The energy level accuracies achieved in the present work are 10%, 3%, and 11% for Nd ii, Nd iii, and Nd iv, respectively, compared to the NIST database. We confirm that the overall properties of the opacity are not significantly affected by the accuracies of the atomic calculations. The impact on the Planck mean opacity is up to a factor of 1.5, which affects the timescale of kilonovae by at most 20%. However, we find that the wavelength-dependent features in the opacity are affected by the accuracies of the calculations. We emphasize that accurate atomic calculations, in particular for low-lying energy levels, are important to provide predictions of kilonova light curves and spectra.

Theoretical investigation of energy levels and transition data for P II

Aims. The main goal of this paper is to present accurate and extensive transition data for the P II ion. These data are useful in various astrophysical applications. Methods. The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, were used in the present work. In the RCI calculations the transverse-photon (Breit) interaction, the vacuum polarization, and the self-energy corrections were included. Results. Energy spectra are presented for 48 even states of the 3s23p2, 3s23p{4p, 4f, 5p, 5f, 6p}, 3s3p23d configurations, and for 58 odd states of the 3s3p3, 3s23p{3d, 4s, 4d, 5s, 5d, 6s} configurations in the P II ion. Electric dipole (E1) transition data are computed between these states along with the corresponding lifetimes. The average uncertainty of the computed transition energies is between five and ten times smaller than the uncertainties from previous calculations. The computed lifetimes for the 3s23p4s3Po states are within the error bars of the most current experimental values.

Negative Ion Formation in Low-Energy Electron Collisions with the Actinide Atoms Th, Pa, U, Np and Pu

Here we investigate ground and metastable negative ion formation in low-energy electron collisions with the actinide atoms Th, Pa, U, Np and Pu through the elastic total cross sections (TCSs) calculations. For these atoms, the presence of two or more open d- and f- subshell electrons presents a formidable computational task for conventional theoretical methods, making it difficult to interpret the calculated results. Our robust Regge pole methodology which embeds the crucial electron correlations and the vital core-polarization interaction is used for the calculations. These are the major physical effects mostly responsible for stable negative ion formation in low-energy electron scattering from complex heavy systems. We find that the TCSs are characterized generally by Ramsauer-Townsend minima, shape resonances and dramatically sharp resonances manifesting ground and metastable negative ion formation during the collisions. The extracted from the ground states TCSs anionic binding energies (BEs) are found to be 3.09eV, 2.98eV, 3.03eV, 3.06eV and 3.25eV for Th, Pa, U, Np and Pu, respectively. Interestingly, an additional polarization-induced metastable TCS with anionic BE value of 1.22eV is generated in Pu due to the size effect. We also found that our excited states anionic BEs for several of these atoms compare well with the existing theoretical electron affinities including those calculated using the relativistic configuration-interaction method. We conclude that the existing theoretical calculations tend to identify incorrectly the BEs of the resultant excited anionic states with the electron affinities of the investigated actinide atoms; this demonstrates the great need for experimental verification and unambiguous determination of their electron affinities.

Multiconfiguration Dirac-Hartree-Fock and configuration-interaction study of 4d−3p x-ray transitions in Cu- and Ni-like tungsten ions

The $4d\ensuremath{\rightarrow}3p$ x-ray transitions in Cu- and Ni-like tungsten ions have been studied theoretically. The multiconfiguration Dirac-Hartree-Fock (MCDHF) method and the large-scale relativistic configuration-interaction (CI) method have been employed in order to take into account electron correlation effects on the wavelengths and transition rates. It was found that the wavelengths and transition rates obtained from the MCDHF-CI method depend strongly on the size and the type of the active space used in the calculations. It has been found that extending the active space of orbitals without careful control of the configuration state function base does not always lead to good quality MCDHF-CI results for highly ionized tungsten ions.