Pseudo-relativistic Hartree-Fock Research Articles

Calculation of forbidden transitions in doubly ionized neodymium (Nd III) of interest for kilonova nebular phase analysis

In this paper, we present new radiative rate calculations for forbidden transitions, namely magnetic dipole (M1) and electric quadrupole (E2) transitions, involving all the experimentally known energy levels within the 4f4 ground configuration of doubly ionized neodymium (Nd III). To do this, and in order to estimate the accuracy of the results obtained, two independent computational approaches based on the pseudo-relativistic Hartree–Fock and the fully relativistic Dirac-Hartree–Fock methods were used. The transition probabilities calculated with these two approaches showed good overall agreement, in particular for the most intense forbidden lines for which the relative differences did not exceed 25%. From these new atomic data, some astrophysical implications were deduced such as the possibility (or not) of observing some [Nd III] lines on the infrared spectra recorded by the James Webb Space Telescope, more precisely for the analysis of nebular phase kilonova spectra following compact object mergers.

Overview of the contributions from all lanthanide elements to kilonova opacity in the temperature range from 25000 to 40000 K

It is now well established that the neutron star (NS) merger is at the origin of the production of trans-iron heavy elements in the universe. These elements are therefore present in large quantities in the ejected matter, whose electromagnetic radiation, called kilonova, is characterized by a significant opacity due to the high density of spectral lines belonging to many heavy ions. Among these, the lanthanide ions play an essential role since, with their open 4f subshell, they have a considerable number of transitions that can absorb emitted light. The knowledge of the atomic structure and the radiative parameters of these ions as well as the determination of the corresponding opacities is therefore of paramount importance for the spectral analysis of kilonovae. The main goal of the present work is to determine the relative contributions of the different lanthanide elements to the opacity of the emission spectrum of a kilonova in its early phase, that is, a few hours after the NS merger, where the conditions are such that the temperature is between 25000 and 40000 K. At these temperatures, the lanthanide ions whose charge states are between V and VII are predominant. We used the pseudo-relativistic Hartree-Fock (HFR) method extensively to calculate the relevant atomic data (energy levels, wavelengths, and oscillator strengths) in La-Lu V-VII ions. The corresponding monochromatic opacities were estimated from the expansion formalism. We calculated the spectroscopic parameters for a total of more than 800 million radiative transitions in all the ions considered. These data were used to estimate the expansion opacities and Planck mean opacities for all the lanthanide elements at early-phase kilonova conditions between 25000 and 40000 K, making it possible to deduce the respective contributions of each element as a function of temperature. Atomic calculations were also carried out with the fully relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) method in the specific case of the Yb V ion, as the available experimental data had not yet been compared with the theoretical calculations in our previous studies on lanthanide ions.

Energy Levels and Transition Data of Cs VI

Previously reported atomic data (spectral lines, wavelengths, energy levels, and transition probabilities) were collected and systematically analyzed for Cs VI. The present theoretical analysis was supported by extensive calculations made for Cs VI with a pseudo-relativistic Hartree–Fock (HFR) method together with the superposition of configuration interactions implemented in Cowan’s codes. In this work, all previously reported energy levels and their (allowed) transition assignments were confirmed. A critically evaluated set of optimized energy levels with their uncertainties, observed and Ritz wavelengths along with their uncertainties, and theoretical transition probabilities with their estimated uncertainties were presented in the compilation. In addition to this, we determined the radiative transition parameters for several forbidden lines within the ground configuration 5s25p2 of Cs VI.

Determination of the radiative transition rates in Ta VII using a multiplatform approach

Tantalum (Z=73) is an element that is produced in the neutron-induced transmutation of tungsten (Z=74) which in turn will compose the divertors in Tokamaks. As a consequence, their sputtering may generate ionic impurities of all possible charge states in the deuterium-tritium plasma that could contribute to radiation losses in controlled nuclear devices. The radiative properties of these ions have therefore potential important applications in this field. In this context, a multiplatform approach has been adopted in order to compute the Ta VII radiative rates and estimate their accuracy. The oscillator strengths and transition probabilities have been calculated for the 237 electric dipole (E1) transitions of the Ta VII spectrum as classified by Ryabtev et al. (2014). Three independent atomic structure models have been used; one based on the semi-empirical pseudo-relativistic Hartree–Fock (HFR) method and two based on the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method.

Atomic data and expansion opacity calculations in two representative 4d transition elements, niobium and silver, of interest for kilonovae studies

Aims. Neutron star (NS) mergers are thought to be a source of heavy trans-iron element production. The latter can be detected in the spectra of the ejected materials, from which bright electromagnetic radiation is emitted. This latter is due to the radioactive decay of the produced heavy r-process nuclei and is known as kilonova. Because of their complex atomic structures – characterized by configurations involving unfilled nd or nf subshells – the heavy elements of the kilonova ejecta often give rise to numerous absorption lines generating significant opacities. The determination of the latter, which are of paramount importance for the analysis of kilonova light curves, requires knowledge of the radiative parameters of the spectral lines belonging to the ions expected to be present in the kilonova ejecta. The aim of the present work is to provide new atomic opacity data for two representative 4d elements, niobium (Nb) and silver (Ag), in their first four charge states, namely for Nb I–IV and Ag I–IV. Methods. Large-scale calculations based on the pseudo-relativistic Hartree-Fock (HFR) method were performed to obtain the atomic structure and radiative parameters while the expansion formalism was used to estimate the opacities. Results. Wavelengths and oscillator strengths were computed for several million spectral lines in Nb I–IV and Ag I–IV ions. The reliability of these parameters was estimated by comparison with the few previously published experimental and theoretical results. The newly obtained atomic data were then used to calculate expansion opacities for typical kilonova conditions expected one day after NS merger, a density of ρ = 10−13 g cm−3, and temperatures ranging from T = 5000 K to T =15 000 K.

Critically Evaluated Atomic Data for the Au iv Spectrum

A spectral investigation of triply ionized gold (Au iv) has been carried out in the wavelength region of 500–2106 Å. The gold spectra were photographed at the National Institute of Standards and Technology, USA, on a 10.7 m normal incidence vacuum spectrograph (NIVS) using a sliding spark source as well as on a 3 m NIVS at the Antigonish laboratory in Canada with a triggered spark source. Our analysis is theoretically supported by the pseudorelativistic Hartree–Fock (HFR) formalism with a superposition of configuration interactions implemented in Cowan's suite of codes. Radiative transition parameters are also calculated using the HFR+CPOL (core polarization effects) model and the multiconfiguration Dirac–Hartree–Fock approach, and their comparisons are used to evaluate the transition rate data. All the previously reported levels of the 5d 8, 5d 76s, and 5d 76p configurations are confirmed, except one, and three are newly established. The missing 1 S 0 level of 5d 8 is now established at 55,277.8 cm−1. A total of 981 observed lines (E1 type), classified to 1031 transitions, including 133 newly identified, enabled us to optimize 139 energy levels. Several astrophysically important transitions, forbidden (M1- and E2-type) lines of 5d 8 and 5d 76s, are provided with their Ritz wavelengths and radiative parameters. A critically evaluated set of energy levels, observed and Ritz wavelengths along with their uncertainties, transition rates, and uniformly scaled intensities of Au iv lines have been presented. Also, large-scale atomic data to compute the opacity of Au iv in the kilonova ejecta have been supplemented in this work.

Expansion and line-binned opacities of samarium ions for the analysis of early kilonova emission from neutron star mergers

ABSTRACTOpacity calculations performed within the expansion and the line-binned formalisms are reported for Sm V–X ions in this paper. These were determined by means of new large-scale atomic structure and radiative rate computations carried out using the pseudo-relativistic Hartree-Fock (HFR) method from which energy levels, wavelengths, and oscillator strengths were deduced for more than 100 millions of spectral lines in the considered samarium ions. In the absence of any experimental data, the reliability of HFR results was roughly estimated by comparison with those obtained with an independent theoretical approach, namely the fully relativistic multiconfiguration Dirac-Hartree-Fock method, in Sm VI and Sm VII. The opacities were estimated for typical conditions corresponding to early phases of kilonovae following neutron star mergers, i.e. for a density ρ = 10−10 g cm−3, a time after the merger t = 0.1 day and temperatures ranging from 25 000 to 70 000 K. In addition, the atomic calculations allowed us to establish the ground level for each of the Sm ions considered (still unknown until now), as well as reliable partition functions that are crucial for the determination of the ionization balance by solving the Saha equation and for accurate opacity calculations.

Opacity calculations in four to nine times ionized Pr, Nd, and Pm atoms for the spectral analysis of kilonovae

ABSTRACT New atomic data for radiative transitions in Pr V–X, Nd V–X, and Pm V–X were determined by means of large-scale calculations involving three independent theoretical methods, i.e. the pseudo-relativistic Hartree–Fock method including core-polarization corrections (HFR+CPOL), the multiconfiguration Dirac–Hartree–Fock (MCDHF) method, and the configuration interaction many-body perturbation theory (CI + MBPT) implemented in the ambit program. This multiplatform approach allowed us to estimate the reliability of the results obtained and to extract a large amount of energy levels, wavelengths, transition probabilities, and oscillator strengths for the determination of opacities required for the analysis of the spectra emitted in the early phases of kilonovae following neutron star mergers, i.e. for typical conditions corresponding to temperatures T > 20 000 K, a density ρ = 10−10 g cm−3, and a time after the merger t = 0.1 d. Our radiative parameters were compared in detail with the few experimental data published so far and their impact on the calculated opacities, in terms of atomic computation strategy, was also examined.

Pseudo-Relativistic Hartree–Fock and Fully Relativistic Dirac–Hartree–Fock Calculations of Radiative Parameters in the Fifth Spectrum of Lutetium (Lu V)

Using two independent theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic Multiconfigurational Dirac–Hartree–Fock (MCDHF) approaches, we computed the radiative parameters (transition probabilities and oscillator strengths) corresponding to the spectrum of quadruply ionized lutetium (Lu V). The agreement observed between both sets of results allowed us to deduce the radiative rates for a large amount of transitions in order to calculate the contribution of this ion to the opacity of kilonovae in their early phases, i.e., for T = 25,000 K. The results obtained were compared to previous data computed for other quadruply ionized lanthanide atoms, namely La V, Ce V, Pr V, Nd V and Pm V, in order to highlight the main contributors to the opacity among these ions under kilonovae conditions where the Vth spectra are predominant.

Energy levels, wavelengths and radiative rates for transitions in Hg-like Bismuth

The fourth spectrum of bismuth (Bi IV) has been investigated in the vacuum ultraviolet region. Recordings of bismuth spectra were made on a 3-m normal incidence vacuum spectrograph at Antigonish laboratory in Canada using a triggered spark light source. The theoretical interpretation for this spectrum was made with the pseudo-relativistic Hartree-Fock approach implemented in Cowan's code. The previous analysis of the energy level structure of Bi IV is confirmed and extended with the identifications of the 6p2 1S0 and 5d96s26p 3D2 levels, which were not reported earlier. Two new doubly excited configurations 6p6d and 6p7s were studied for the first time with the identification of 56 spectral lines. In total, 84 energy levels were located in the 5d10[6s2+ 6snp (n = 6, 7) + 6p2 + 6snd (n = 6, 7) + 6s5f], 6p6d, 6p7s, 5d96s2np (n = 6–10) and 5d96s2nf (n = 5–13) configurations, among which fifteen were newly established. A total of 552 spectral lines have now been classified in Bi IV in the region 193–5000 Å. We also present the optimized energy level values, transition rates and Ritz wavelengths along with their uncertainties evaluated using the least-squares fitting procedure.

Atomic structure of the doubly ionized titanium Ti III ion

In this work, the atomic structure of Ti III is calculated using two methods, the Thomas-Fermi–Dirac-Amaldi (TFDA) method using the AUTOSTRUCTURE (AS) atomic structure code and the pseudo-relativistic Hartree–Fock (HFR) method using the Cowan (CW) atomic structure code. We used the terms and levels generated by the 19 configurations: 3p6 3d2, 3dns (n = 4–7), 3dnp (n = 4–7), 3dnd (n = 4–7), 3d nf (n = 4–7), 3p6 4s2,3p6 4s4p. Our calculated values are compared with available experimental and theoretical results and new theoretical data of our own are obtained.

Experimental and Theoretical Radiative Parameters of Highly Excited Odd-parity Levels in Ir ii

Using the time-resolved laser-induced fluorescence technique, the radiative lifetimes for 15 odd-parity levels from 47,003 to 61,475 cm−1 in Ir ii were measured. To the best of our knowledge, 11 lifetime results among these levels are reported for the first time, and hence they should be a good complement to the measured lifetime data of 10 levels previously published in the literature. The pseudorelativistic Hartree–Fock including core-polarization corrections method was used to calculate the lifetimes and branching fractions (BFs) of the investigated energy levels. Combining the experimental lifetime with the theoretical BFs, the transition probabilities and oscillator strengths for 124 transitions were determined.

Measurements and Calculations of Radiative Parameters for Odd-parity Levels in Nb ii

Abstract Experimental radiative lifetimes for 34 odd-parity levels belonging to 4d 35p and 4d 25s5s configurations of Nb ii were measured by the time-resolved laser-induced fluorescence method. The results range from 2.2 to 11.5 ns, and 30 of them were reported for the first time, as far as we know. The theoretical radiative lifetimes for these levels were also calculated by the pseudorelativistic Hartree–Fock method including core-polarization contributions (HFR+CPOL) and the fully relativistic multiconfiguration Dirac–Hartree–Fock method, and branching fractions for these levels were also calculated by HFR+CPOL. By combining the experimental lifetimes and the calculated branching fraction values, the semiempirical transition probabilities and oscillator strengths for 389 Nb ii lines were obtained.

Experimental and Theoretical Radiative Parameters of Highly Excited Levels in Re ii

Abstract Natural radiative lifetimes of 22 odd-parity levels of Re ii in the energy range between 43,937.7 and 65,572.3 cm−1 were measured by the time-resolved laser-induced fluorescence method. To our knowledge, the lifetimes for 18 out of 22 levels were measured for the first time. The theoretical radiative lifetimes and branching fractions (BFs) for these levels were obtained from pseudorelativistic Hartree–Fock calculations including core-polarization effects. By combining the experimental lifetimes and calculated BFs, a set of semiempirical transition probabilities and oscillator strengths for 232 Re ii lines were determined. The radiative parameters obtained in the present work will greatly enrich the atomic database of Re ii and hence are expected to be helpful for astrophysicists in Re abundance evaluation of stars.

Radiative lifetimes, branching fractions, and oscillator strengths for highly excited levels in singly ionized tantalum (Ta ii)

ABSTRACT Radiative lifetimes of 28 levels of Ta ii in the energy range 29256.907–55128.389 cm−1 were measured by time-resolved laser-induced fluorescence (TR-LIF) spectroscopy in laser-ablation plasma. Among the results, to our knowledge, 24 lifetimes are reported for the first time. These lifetimes, ranging from 2.7 to 111 ns, were combined with theoretical branching fractions obtained from pseudo-relativistic Hartree–Fock calculations including core-polarization effects to deduce semi-empirical transition probabilities and oscillator strengths for 284 Ta ii spectral lines.

Energy structure investigations in triply ionized mercury: Hg IV

We report energy level structure of triply ionized mercury (Hg IV). The spectrum was recorded on a 3-m normal incidence vacuum spectrograph in the wavelength region 300 – 2000 Å, using a triggered spark source at the spectroscopy laboratory, St. Francis Xavier University, Antigonish in Canada. Wavelength measurement and the corresponding uncertainties caused by calibration procedures are carefully analyzed. Based on the analysis of original measurements, the energy levels are optimized, which resulted in an improved set of energy level values. A complete disentanglement of the origin of these energy levels may well be impossible; therefore, new configurations have been extended in our theoretical calculations using Cowan's pseudo-relativistic Hartree-Fock code with superposition of interacting configurations. All preceding results were confirmed, and the 5d8(6d + 7s) mixed configurations have been newly established with the aid of experimental data supported by theoretical calculations. Along with the optimized energy eigenvalues, the observed and Ritz wavelengths, transition rates, and eigenvector compositions of Hg IV are also given. The energy level values were optimized using a computer code LOPT.

Radiative parameters of high-lying levels in neutral rhodium

ABSTRACT Radiative lifetimes of 20 high-lying excited levels in neutral rhodium (Rh i) were measured using time-resolved laser-induced fluorescence technique, 17 of which are reported for the first time to our knowledge. These lifetimes were combined with theoretical branching fractions obtained from pseudo-relativistic Hartree–Fock calculations to deduce semi-empirical transition probabilities and oscillator strengths for 63 Rh i spectral lines.

Energy structure and radiative parameter calculations in the Re-like Pt IV, Au V and Hg VI spectra and preliminary line identifications in Hg VI

We performed extended ab-initio atomic structure calculations for Ir III-like Pt IV, Au V and Hg VI by using the pseudo-relativistic Hartree-Fock approach (HFR). These computations yielded theoretical energy levels and transition data for the electric dipole (E1) transitions. The results obtained in this study compare well with the available experimental data. More precisely, the good agreement of our theoretical calculations with experimental values for Pt IV and Au V allowed us to execute precise calculations for Hg VI by scaling the Slater parameters similar to Au V which is next to Hg VI in Re isoelectronic sequence. Most of our computed energy levels and radiative transition rates for Re-like Hg VI were not reported before. We provide accurate and comprehensive atomic data related to this ion that could be used by astrophysicists for interpretation of stellar spectra. On the basis of these calculations, preliminary identifications of 32 strong Hg VI lines were made in our experimental spectrograms.

Spectral analysis and calculations of line parameters for Xe-like Ce V

Four-times ionized cerium (Ce V) is isoelectronic with neutral xenon, having 5s25p6 1S0, the only level in the ground configuration. Previously reported energy levels and line classifications of the 5s25p5 (4f+5d+6d+6s and 6p) configurations were evaluated empirically by means of extended calculations and Boltzmann plots. Here, we have added a new configuration 5s5p64f to the previously reported work. The spectrum was recorded on a 3 m normal incidence vacuum spectrograph in the 300–1240 Å region at the Antigonish laboratory (Canada). Theoretical calculations were performed using the pseudo-relativistic Hartree-Fock (HFR) configuration interaction method. The transition probabilities were calculated for the above-mentioned configurations. We also calculated the lifetimes of 5s25p54f metastable states using the MCDHF method.

Spectral line list of potential cosmochronological interest deduced from new calculations of radiative transition rates in singly ionized thorium (Th ii)

ABSTRACTIn this work, we report a list of 91 strong Th ii spectral lines in the visible wavelength region that could be used as cosmochronometers in future investigations to determine stellar ages from thorium radioactive decay. This list was established on the basis of a pseudo-relativistic Hartree–Fock model including core-polarization corrections (HFR+CPOL) allowing us to compute the corresponding radiative decay parameters, the latter being found to be in good overall agreement with the most accurate experimental data when available. Besides this semi-empirical approach, the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method was attempted, showing large discrepancies with both the present HFR+CPOL and the most recent experimental oscillator strengths, although the calculated wavelengths from theoretical energy levels agreed with observed spectral line wavelengths within 2.4 per cent.