1s2s 3S Research Articles

Probing Collins Conjecture with correlation energies and entanglement entropies for the ground and excited states in the helium iso‐electronic sequence

AbstractIn the present work, we present an investigation of Collins Conjecture, a hypothesis made by D. M. Collins in 1993 relating correlation energy and entanglement entropy, by calculating the ground state and singly‐excited triplet‐spin 1s2s 3S and 1s3s 3S state energies of the helium iso‐electronic sequence, with Z = 2–15. By using extensive orthonormal configuration interaction (CI) type wave functions with B‐Spline basis up to about 6000 terms, linear entropy and von Neumann entropy for the abovementioned atomic systems are determined. Together with the Hartree‐Fock energies obtained following a self‐consistent field theory, we have found that there exist linearly proportionalities between the renormalized correlation energies and entanglement entropies of both linear and von Neumann, showing a support for Collins Conjecture applicable to the ground and singly‐excited triplet‐spin states in the helium sequence, for a range of finite Z‐values.

Investigating the Impact of Atomic Data Uncertainties on the Measured Physical Parameters of the Perseus Galaxy Cluster

Accurate atomic data and plasma models are essential for interpreting the upcoming high-quality spectra from missions like XRISM and Athena. Estimating physical quantities, like temperature, abundance, turbulence, and the resonance scattering factor, is highly dependent on the underlying atomic data. We use the AtomDB tool variableapec to estimate the impact of atomic data uncertainties in Einstein A coefficients, collisional rate coefficients, and the ionization and recombination rates of H-, He-, and Li-like iron in modeling the spectrum of Perseus observed by Hitomi. The best-fit temperatures, abundances, resonance scattering factors, and turbulence parameters including atomic data uncertainties vary by approximately 17%, 35%, 30%, and 3%, respectively, from the best-fit temperatures, abundances, RS factors, and turbulence parameters estimated without atomic data uncertainties. These indicate that approximately 32%, 35%, and 25% of the best-fit temperatures, abundances, and resonance scattering factors when including uncertainties lie outside the 3σ error regions of their corresponding best-fit values computed with zero atomic data errors. Expanding the energy range to 1.8–20.0 keV shows less variability, with 26% of the abundances and 22% of the resonance scattering factors lying outside the 3σ errors of the best-fit values. We also studied correlations between physical parameters and atomic rate uncertainties to identify key atomic quantities requiring precise lab measurements. We report negative correlations between the best-fit temperatures and the z (1s2s 3S1 → 1s2) collisional rate coefficients, abundances and y (1s2p 3P1 → 1s2) collisional rate coefficients, and abundances and z collisional rate coefficients, and a positive correlation between the resonance scattering factors and the w (1s2p 1P1 → 1s2) collisional rate coefficients.

RELATIVISTIC APPROACH TO COMPUTING WAVELENGTHS OF TRANSITIONS IN SPECTRA OF ATOMIC SYSTEMS IN PLASMAS

New relativistic approach to computing the spectral parameters of multicharged ions in plasmas for different values of the plasmas screening (Debye) parameter (respectively, electron density, temperature) is presented. The presented approach is based on the generalized relativistic energy approach combined with the optimized relativistic many-body perturbation theory with the Dirac-Debye screening hamiltonian as a zeroth approximation, adapted for application to study the energy and spectral parameters of atoms and ions in plasmas. The special exchange potential as well as the electron density with dependence upon the temperature are used. The wavelengths for a number of transitions, including (A): E(1s2p 1P1)-E(1s2 1S); (B) E(1s3p 1P1)_E(1s2 1S); (C)AK: E(1s2p 3P1)_E(1s2s 3S); (D): E(1s3p 3P1)_E(1s2s 3S) of the helium in plasmas for various Debye lengths are calculated and compared with the corresponding data by Kar-Ho.

Radiative Cascade Repopulation of 1s2s2p 4P States Formed by Single Electron Capture in 2–18 MeV Collisions of C4+ (1s2s 3S) with He

This study focuses on the details of cascade repopulation of doubly excited triply open-shell C3+(1s2s2p)4P and 2P± states produced in 2–18 MeV collisions of C4+(1s2s3S) with He. Such cascade calculations are necessary for the correct determination of the ratio R of their cross sections, used as a measure of spin statistics [Madesis et al. PRL 124 (2020) 113401]. Here, we present the details of our cascade calculations within a new matrix formulation based on the well-known diagrammatic cascade approach [Curtis, Am. J. Phys. 36 (1968) 1123], extended to also include Auger depopulation. The initial populations of the 1s2snℓ4L and 1s2snℓ2L levels included in our analysis are obtained from the direct nℓ single electron capture (SEC) cross sections, calculated using the novel three-electron close-coupling (3eAOCC) approach. All relevant radiative branching ratios (RBR) for n≤4 were computed using the COWAN code. While doublet RBRs are found to be very small, quartet RBRs are found to be large, indicating cascade feeding to be important only for quartets, consistent with previous findings. Calculations including up to third order cascades, extended to n→∞ using an n−3 SEC model, showed a ∼60% increase of the 1s2s2p4P populations due to cascades, resulting, for the first time, in R values in good overall agreement with experiment.

Linear polarization of anisotropically excited x-ray lines from the n = 2 complex in He-like Ar16+

High-resolution x-ray spectra were recorded at the National Institute of Standards and Technology electron beam ion trap (EBIT) using two Johann-type crystal spectrometers, with their dispersion planes oriented parallel and perpendicular to the beam direction. The linear polarizations of the 1s2 − 1s2l transitions in He-like argon ions were determined from the measured spectra at electron beam energies of 3.87 and 7.91 keV. The theoretical analysis was performed using detailed collisional-radiative modeling of the non-Maxwellian EBIT plasma with the NOMAD code modified to account for magnetic sublevel atomic kinetics. Effects influencing the polarizations of the observed 1s2 − 1s2l lines were investigated, including radiative cascades, the 1s2 1S0 − 1s2s 1S0 two-photon transition, and the charge exchange recombination of H-like argon ions. With these included, the measured polarizations of the resonance (1s2 1S0 − 1s2p 1P1), intercombination (1s2 1S0 − 1s2p 3P1), and forbidden lines (1s2 1S0 − 1s2s 3S1, 1s2 1S0 − 1s2p 3P2 ) were found to be in good agreement with the calculations.

Most Intense X-Ray Lines of the Helium Isoelectronic Sequence for Plasmas Diagnostic

We report accurate wavelengths for the three most intense lines (resonance line: 1s2 1S0 - 1s2p 1P1, intercombination line: 1s2 1S0 - 1s2p 3P1 and forbidden line: 1s2 1S0 - 1s2s 3S1) along with wavelengths for the 1s2 1S0 - 1snp1P1 and 1S0 - 1snp3P2 (2 ≤ n ≤ 25) transitions in He-like systems (Z = 2 – 13). The first spectral lines that belong to the above transitions are established in the framework of the Screening Constant per Unit Nuclear Charge method. The results obtained agree excellently with various experimental and theoretical literature data. The uncertainties in wavelengths between the present calculations and the available literature data are less than 0.004Å. A host of new data listed in this paper may be of interest in astrophysical and laboratory plasmas diagnostic.

Li-like carbon Auger KLL measurements of mixed-state C4+(1s2 1S, 1s2s 3S) ions in 6-15 MeV collisions with He and comparison to 3eAOCC calculations

SynopsisNew state-resolved Li-like carbon Auger KLL measurements of mixed-state C4+(1s2 1S, 1s2s 3S) ions in 6-15 MeV collisions with He are presented. Results of three-electron semiclassical atomic orbital AOCC coupled channel (3eAOCC) calculations are also presented and compared.

Installation of a gas terminal stripper and a gas/foil post stripper system at the 5.5 MV Demokritos Tandem Van de Graaff accelerator

A gas stripper system has been installed inside the terminal of the Demokritos TANDEM accelerator, in addition to the existing foil stripper system, while two additional post strippers (one gas and one foil) were also installed in the beam line between the analyzing and switching magnets of the accelerator. These installations were necessary for the production of He-like ion beams used in the APAPES‡ project for the investigation of electron capture phenomena in ion-atom collisions using high resolution zero-degree Auger projectile electron spectroscopy in a dedicated experimental setup already in operation since two years. Older measurements have shown that for He-like ion beams foil stripping results in the production of a mixed-state beam (1s2, 1s2s 3S), while gas stripping in the terminal can produce an almost pure ground-state (1s2) beam. Thus, using both strippers, collision measurements will allow for the selective determination of state-selective capture contributions from either the metastable- (1s2s 3S) or the ground-state of the ion by judicious analysis of both associated projectile K-Auger electron spectra. In addition, post-stripping will allow us to obtain ion charge states whose production is not possible with only one stage of stripping.

Near-infrared Zeeman spectroscopy for the spatially resolved measurement of helium emission spectra in Heliotron J

A passive spectroscopic method that can measure spatially resolved emission spectra only by observing from a single diagnostic port without assuming plasma symmetry was applied to the stellarator-heliotron device Heliotron J. The emission spectra from the inboard and outboard sides were separated using the difference in their Zeeman effects. On the basis of the fact that in a spectrum as a function of the wavelength, the magnitude of the wavelength splitting by the Zeeman effect relative to the Doppler broadening increases with the wavelength, the method was applied to a near-infrared helium emission line (He I 1s2s 3S−1s2p 3P, 1083 nm), and it was confirmed that the uncertainty in the separated spectra was reduced compared with that in the application to visible emission lines. From the emissivity of the separated spectra, the local recycling flux was evaluated using the inverse photon efficiency method.

Photoionization of metastable heliumlike C4+(1s2sS13) ions: Precision study of intermediate doubly excited states

In a joint experimental and theoretical endeavour, photoionization of metastable C4+(1s 2s 3S1) ions via intermediate levels with hollow, double-K-vacancy configurations 2s2p, 2s3p, 2p3s, 2p3d, 2s4p, 2p4s and 2p4d has been investigated. High-resolution photon-ion merged-beams measurements were carried out with the resolving power reaching up to 25,000 which is sufficient to separate the leading fine-structure components of the 2s2p 3P term. Many-body perturbation theory was employed to determine level-to-level cross sections for K-shell excitation with subsequent autoionization. The resonance energies were calculated with inclusion of electron correlation and radiative contributions. Their uncertainties are estimated to be below $\pm$1 meV. Detailed balance confirms the present photoionization cross-section results by comparison with previous dielectronic-recombination measurements. The high accuracy of the theoretical transition energies together with the present experimental results qualify photoabsorption resonances in heliumlike ions as new, greatly improved energy-reference standards at synchrotron radiation facilities.

Relativistic calculations of fine-structure energy levels of He-like Ar in dense plasmas**Project supported by the National Natural Science Foundation of China (Grant No. 11474208) and the Doctoral Science Foundation of Longdong University, China (Grant No. XYBY1704).

The fine-structure energy levels of 1s2s and 1s2p atomic states for the He-like Ar ion immersed in dense plasmas are calculated. The ion sphere model is used to describe the plasma screening effect on the tested ion. The influences of the hard sphere confinement and plasma screening on the fine-structure energy levels are investigated respectively. The calculated results show that the confined effect of the hard sphere on the fine-structure energy levels increases with decreasing hard sphere radius, and the plasma screening effect on the fine-structure energy levels increases with the increase of free electron density. In dense plasmas, the confined effect of the hard sphere on the fine-structure energy levels can be neglected generally, compared with the contribution from free electron screening. An interesting phenomenon about the energy level crossing is found among 1s2s (1S0) and 1s2p (3P0,1) atomic states. The results reported at the present work are useful for plasma diagnostics.

Penning ionization widths by Fano-algebraic diagrammatic construction method.

We present an ab initio theory and computational method for Penning ionization widths. Our method is based on the Fano theory of resonances, algebraic diagrammatic construction (ADC) scheme for many-electron systems, and Stieltjes imaging procedure. It includes an extension of the Fano-ADC scheme [V. Averbukh and L. S. Cederbaum, J. Chem. Phys. 123, 204107 (2005)] to triplet excited states. Penning ionization widths of various He*-H2 states are calculated as a function of the distance R between He* and H2. We analyze the asymptotic (large-R) dependences of the Penning widths in the region where the well-established electron transfer mechanism of the decay is suppressed by the multipole- and/or spin-forbidden energy transfer. The R-12 and R-8 power laws are derived for the asymptotes of the Penning widths of the singlet and triplet excited states of He*(1s2s1,3S), respectively. We show that the electron transfer mechanism dominates Penning ionization of He*(1s2s 3S)-H2 up until the He*-H2 separation is large enough for the radiative decay of He* to become the dominant channel. The same mechanism also dominates the ionization of He*(1s2s 1S)-H2 when R < 5 Å. We estimate that the regime of energy transfer in the He*-H2 Penning ionization cannot be reached by approaching zero collisional temperature. However, the multipole-forbidden energy transfer mechanism can become important for Penning ionization in doped helium droplets.

Competition between radiative and Auger decay processes of doubly excited Li-like C, N and O ions

SynopsisWe performed charge exchange collision experiments of metastable He-like C, N and O ions (1s2s 3S1) with neutral target gases, and observed soft X-rays from doubly excited Li-like C, N and O ions produced by single electron capture. These emissions corresponded to 1s22s 1S0 - 1s2s (3S1) np transitions according to calculations for transition energies by the Cowan code.

Accessing the hyperfine splitting in highly charged helium-like ions via angle-resolved x-ray spectroscopic analysis

SynopsisA new scheme is presented for determining the hyperfine splitting of highly charged ions via angle-resolved spectroscopic analysis. In particular, we propose two measurements on the angular distribution and linear polarization of the emission line 1s2p 3P1, F = I − 1, I, I + 1 → 1s2 1S0, Ff = I of He-like isotopic ions, following the stimulated decay of the 1s2s 1S0, Fi = I level. We find that the angular and polarization behavior of the emitted photons strongly depends on the splitting of the overlapping hyperfine 1s2p 3P1, F resonances, which could be a promising “signature” for the hyperfine splitting determination.

X-ray diffraction patterns and diffracted intensity of Kα spectral lines of He-like ions

In the present paper, we have calculated fine-structure energy levels related to the configurations 1s2s, 1s2p, 1s3s and 1s3p by employing GRASP2K code. We have also computed radiative data for transitions from 1s2p 1P1o, 1s2p 3P2o, 1s2p 3P1o and 1s2s 3S1 to the ground state 1s2. We have made comparisons of our presented energy levels and transition wavelengths with available results compiled by NIST and good agreement is achieved. We have also provided X-ray diffraction (XRD) patterns of Kα spectral lines, namely w, x, y and z of Cu XXVIII, Kr XXXV and Mo with diffraction angle and maximum diffracted intensity which is not published elsewhere in the literature. We believe that our presented results may be beneficial in determination of the order parameter, X-ray crystallography, solid-state drug analysis, forensic science, geological and medical applications.

Evidence for the non-statistical population of the 1s2s2p4P metastable state by electron capture in 4 MeV collisions of B3+(1s2s 3S) with H2 targets

We have revisited previously published data involving collisions of mixed 4MeV B3+(1s21S,1s2s3S) with H2 targets (Benis et al., 2002) in search of evidence for the non-statistical production of the 1s2s2p4P long-lived metastable state by single electron capture. Using our recently published method for the accurate determination of the effective solid angle of Auger decaying metastable projectile states in combination with knowledge of the 1s2s3S metastable beam fraction allowed us to determine the ratio R=4P/2P of 1s2s2p quartet to doublet production cross sections both formed by electron capture. Our present determination of R=2.8±0.5, clearly departs from the expected value of R=2 based on statistical spin recoupling arguments and thus provides evidence for the active presence of additional population mechanisms in a new collision system.

Weak- and hyperfine-interaction-induced 1s2s 1S0 → 1s2 1S0 E1 transition rates of He-like ions**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274254, 11147108, 10979007, U1331122, and U1332206) and in part by the National Basic Research Program of China (Grant No. 2013CB922200).

Weak- and hyperfine-interaction-induced 1s2s 1S0 → 1s2 1S0 E1 transition rates for the isoelectronic sequence of He-like ions have been calculated using the multi-configuration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction methods. The results should be helpful for the future experimental investigations of parity non-conservation effects.

Direct and indirect processes in electron-impact ionization of 1s2 1S0 ground-state and 1s2s 3S1 metastable He-like N5+ ions

Absolute cross sections for electron-impact ionization of two-electron N5+ ions in the 1s2 1S0 ground state and in the 1s2s 3S1 metastable state have been measured. Spectroscopic-quality electron-energy scans were obtained revealing the details of indirect ionization mechanisms which contribute to net single ionization of the metastable, K-shell excited parent N5+(1s2s) ion.

Photoionization of metastable state 1s2s 1S0 of helium

The interference effects between the direct and indirect photoionization processes from the metastable state 1s2s 1S0 of helium are studied by employing the multi-configuration Dirac-Fock (MCDF) method combining with the Fano parameterization technique. Good agreement is found between the present calculations and the available experimental results. It is shown that the interference effects, which further modified the direct photoionization cross sections even far away from the resonances, play an important role in reproducing the resultant nonresonant background beside the configuration interaction in bound ionic states.

Simultaneous electron–photon excitation of helium in an Nd:YAG laser field

R-matrix Floquet theory is used to study the laser-assisted electron-impact excitation of helium at collision energies close to the He(1s2ℓ) thresholds in the presence of a Nd:YAG laser field of intensity 1010 W cm−2. A strong ac Stark mixing occurs between the 1s2s 3S and 1s2p 3Po states. The He−(1s2s2 2S) resonance gives rise to a series of structures in the integrated cross sections, in particular a dominant peak below the first excitation threshold. Agreement with experiment is very good at low energies, but at higher energies, the calculated signal remains small while the experimental results are very negative. The role of multiphoton ionization of the metastable states by the Nd:YAG laser field as a mechanism for signal loss in the experiment is also investigated.