Atomic Structure Calculations Research Articles

Determination of the isotopic change in nuclear charge radius from extreme-ultraviolet spectroscopy of highly charged ions of Xe

The electron-beam ion trap (EBIT) at the National Institute of Standards and Technology (NIST) was employed for the measurement and detailed analysis of the $\ensuremath{\delta}\ensuremath{\lambda}(^{124}\mathrm{Xe},^{136}\mathrm{Xe})$ isotopic shifts of the Al-like $3{s}^{2}3p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}\ensuremath{-}3{s}^{2}3p\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$, Al-like $3{s}^{2}3p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}\ensuremath{-}3{s}^{2}3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$, Mg-like $3{s}^{2}\phantom{\rule{4pt}{0ex}}^{1}S_{0}\ensuremath{-}3s3p\phantom{\rule{4pt}{0ex}}^{1}P_{1}$, Mg-like $3{s}^{2}\phantom{\rule{4pt}{0ex}}^{1}S_{0}\ensuremath{-}3s3p\phantom{\rule{4pt}{0ex}}^{3}P_{1}$, Na-like $3s\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}\ensuremath{-}3p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}$ (${D}_{1}$), and Na-like $3s\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}\ensuremath{-}3p\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$ (${D}_{2}$) transitions. Systematic analysis revealed possible line blends and contributing experimental uncertainties. Highly accurate atomic-structure calculations were conducted and used to determine the $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{136,124}$ difference in the mean-square nuclear charge radii of the two xenon isotopes. In the present work, $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{136,124}$ of 0.276 $\ifmmode\pm\else\textpm\fi{}$ 0.030 ${\mathrm{fm}}^{2}$ was obtained from the weighted average of the Na-like ${D}_{1}$, Mg-like $3{s}^{2}\ensuremath{-}3s3p$ and Al-like $3{s}^{2}3p\ensuremath{-}3{s}^{2}3p$ and $3{s}^{2}3p\ensuremath{-}3{s}^{2}3d$ transitions. This result confirms the value previously determined from the Na-like ${D}_{1}$ transition of 0.269 $\ifmmode\pm\else\textpm\fi{}$ 0.042 ${\mathrm{fm}}^{2}$. The uncertainty of our result is half of that of previous results for the same isotopes obtained from x-ray spectroscopy of muonic atoms, laser spectroscopy of neutral xenon atoms, and a global evaluation of charge radii. Our result is slightly outside the uncertainty of the value obtained from a King plot analysis of comparable precision. The present work illustrates that extreme-ultraviolet spectroscopy of highly charged ions is a viable approach for measurements of charge nuclear radii differences and can be used to benchmark conventional methods.

Structural trends in atomic nuclei from laser spectroscopy of tin

Tin is the chemical element with the largest number of stable isotopes. Its complete proton shell, comparable with the closed electron shells in the chemically inert noble gases, is not a mere precursor to extended stability; since the protons carry the nuclear charge, their spatial arrangement also drives the nuclear electromagnetism. We report high-precision measurements of the electromagnetic moments and isomeric differences in charge radii between the lowest 1/2+, 3/2+, and 11/2− states in 117–131Sn, obtained by collinear laser spectroscopy. Supported by state-of-the-art atomic-structure calculations, the data accurately show a considerable attenuation of the quadrupole moments in the closed-shell tin isotopes relative to those of cadmium, with two protons less. Linear and quadratic mass-dependent trends are observed. While microscopic density functional theory explains the global behaviour of the measured quantities, interpretation of the local patterns demands higher-fidelity modelling.

Systematic opacity calculations for kilonovae

ABSTRACTCoalescence of neutron stars (NSs) gives rise to kilonova, thermal emission powered by radioactive decays of freshly synthesized r-process nuclei. Although observational properties are largely affected by bound–bound opacities of r-process elements, available atomic data have been limited. In this paper, we study element-to-element variation of the opacities in the ejecta of NS mergers by performing systematic atomic structure calculations of r-process elements for the first time. We show that the distributions of energy levels tend to be higher as electron occupation increases for each electron shell due to the larger energy spacing caused by larger effects of spin–orbit and electron–electron interactions. As a result, elements with a fewer number of electrons in the outermost shells tend to give larger contributions to the bound–bound opacities. This implies that Fe is not representative for the opacities of light r-process elements. The average opacities for the mixture of r-process elements are found to be κ ∼ 20–30 cm2 g−1 for the electron fraction of Ye ≤ 0.20, κ ∼ 3–5 cm2 g−1 for Ye = 0.25–0.35, and κ ∼ 1 cm2 g−1 for Ye = 0.40 at $T = 5000\!-\!10\, 000$ K, and they steeply decrease at lower temperature. We show that, even with the same abundance or Ye, the opacity in the ejecta changes with time by one order of magnitude from 1 to 10 d after the merger. Our radiative transfer simulations with the new opacity data confirm that ejecta with a high electron fraction (Ye ≳ 0.25, with no lanthanide) are needed to explain the early, blue emission in GW170817/AT2017gfo while lanthanide-rich ejecta (with a mass fraction of lanthanides ∼5 × 10−3) reproduce the long-lasting near-infrared emission.

Modeling kilonova emission from neutron star mergers

AbstractCoalescence of binary neutron stars gives rise to kilonova, thermal emission powered by radioactive decays of newly synthesized r-process nuclei. Observational properties of kilonova are largely affected by bound-bound opacities of r-process elements. It is, thus, important to understand atomic properties of heavy elements to link the observed signals with nucleosynthesis of neutron star mergers. In this paper, we introduce the latest status of kilonova modeling by focusing on the aspects of atomic physics. We perform systematic atomic structure calculations of r-process elements to understand element-to-element variation in the opacities. We demonstrate that the properties of the atomic structure of heavy elements are imprinted in the opacities of the neutron star merger ejecta and consequently in the kilonova light curves and spectra. Using this latest opacity dataset, we briefly discuss implications for GW170817, expected diversity of kilonova emission, and prospects for element identification in kilonova spectra.

Stopping power of hydrogen in hafnium and the importance of relativistic 4f electrons

The stopping power of protons through Hf foil has been studied both experimentally and theoretically. The measurements were performed at the Laboratory of Accelerators and X-Ray Diffraction in Lisbon by using the transmission method on self-supporting stopping material. The overall uncertainty of around $5%$ was established over the protons energy range (0.6--2.5) MeV. The theoretical developments involved fully relativistic atomic structure calculations for Hf, which required the solution of the Dirac equation. The shell-wise local plasma approximation was used to describe the energy transferred to the bound $1s\text{\ensuremath{-}}4f$ electrons, and the outer four electrons were considered as a free electron gas. We found the relativistic description of the $4f$ shell and the screening between $4f$ and $5p$ electrons to be decisive around the stopping maximum. Present theoretical and experimental results are in very good agreement in the energy region of the new measurements. However, our theoretical stopping cross sections show substantial differences with the most used semiempirical models (SRIM2013 and ICRU-49) at intermediate to low energies. Our calculations suggest the stopping maximum to be higher and shifted to lower energies than these previous predictions. Future measurements around the maximum and below would be necessary for a better understanding of the stopping power of hafnium.

Detection of metastable electronic states by Penning trap mass spectrometry.

State-of-the-art optical clocks1 achieve precisions of 10-18 or better using ensembles of atoms in optical lattices2,3 or individual ions in radio-frequency traps4,5. Promising candidates for use in atomic clocks are highly charged ions6 (HCIs) and nuclear transitions7, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range8 that are accessible to frequency combs9. However, insufficiently accurate atomic structure calculations hinder the identification of suitable transitions in HCIs. Here we report the observation of a long-lived metastable electronic state in an HCI by measuring the mass difference between the ground and excited states in rhenium, providing a non-destructive, direct determination of an electronic excitation energy. The result is in agreement with advanced calculations. We use the high-precision Penning trap mass spectrometer PENTATRAP to measure the cyclotron frequency ratio of the ground state to the metastable state of the ion with a precision of 10-11-an improvement by a factor of ten compared with previous measurements10,11. With a lifetime of about 130 days, the potential soft-X-ray frequency reference at 4.96×1016 hertz(corresponding to a transition energy of 202 electronvolts) has a linewidth of only 5×10-8 hertz and one of the highest electronic quality factors (1024) measured experimentally so far. The low uncertainty of our method will enable searches for further soft-X-ray clock transitions8,12 in HCIs, which are required for precision studies of fundamental physics6.

Revised and extended calculations with relativistic and QED corrections of selected He-like 3d-elemental ions having astrophysical significance

We have systematically enlarged Multiconfiguration Dirac-Fock wavefunctions for the relativistic configuration interaction calculation to include the Breit interaction and quantum electrodynamic corrections for evaluating fine structure data of He-like ions having non-zero nuclear spin for five 3d group elements Scandium, Vanadium, Manganese, Cobalt and Copper. Computed energy levels, transition probabilities, oscillator strengths and x-ray wavelengths are compared with the available experimental values and theoretical computations. Special emphasis is given on the forbidden transition rates and hyperfine structure calculations as they are of potential interest in astrophysics. An attempt is made to study the individual contributions of the relativistic effects through Breit interaction and the quantum electrodynamic corrections such as vacuum polarization and self-energy correction to the line strengths useful for plasma diagnostic studies relevant to astrophysics. • Atomic structure calculation is done using Multiconfiguration Dirac-Fock method. • Relativistic configuration interaction calculation is used to report atomic data. • Impacts of relativistic and QED corrections on line strengths are discussed. • Hyperfine coupling constants A J & B J are evaluated for plasma diagnostic studies. • Computed atomic data for He-like odd Z 3d ions are compared with available data.

Multiple Photodetachment of Carbon Anions via Single and Double Core-Hole Creation.

We report on new measurements of m-fold photodetachment (m=2-5) of carbon anions via K-shell excitation and ionization. The experiments were carried out employing the photon-ion merged-beams technique at a synchrotron light source. While previous measurements were restricted to double detachment (m=2) and to just the lowest-energy K-shell resonance at about 282eV, our absolute experimental m-fold detachment cross sections at photon energies of up to 1000eV exhibit a wealth of new thresholds and resonances. We tentatively identify these features with the aid of detailed atomic-structure calculations. In particular, we find unambiguous evidence for fivefold detachment via double K-hole production.

Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals

A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via fractionally occupied orbitals. Specialized versions of Hartree-Fock as well as local density and generalized gradient approximation density functionals are developed, allowing extremely rapid calculations at the basis set limit on the ground and low-lying excited states even for heavy atoms. The implementation of range-separation based on the Yukawa or complementary error function (erfc) kernels is also described, allowing complete basis set benchmarks of modern range-separated hybrid functionals with either integer or fractional occupation numbers. Finally, computation of atomic effective potentials at the local density or generalized gradient approximation levels for the superposition of atomic potentials (SAP) approach [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)] that has been shown to be a simple and efficient way to initialize electronic structure calculations is described. The present numerical approach is shown to afford beyond microhartree accuracy with a small number of numerical basis functions, and to reproduce literature results for the ground states of atoms and their cations for $1 \leq Z \leq 86 $. Our results indicate that the literature values deviate by up to 10 {\mu}Eh from the complete basis set limit. The numerical scheme for the erfc kernel is shown to work by comparison to results from large Gaussian basis set calculations from the literature. Spin-restricted ground states are reported for Hartree-Fock and Hartree-Fock-Slater calculations with fractional occupations for $1 \leq Z \leq 118$.

Modelling hyperfine interactions for nuclear g-factor measurements

A promising technique forg-factor measurements on short-lived nuclear states utilises the hyperfine fields of free ions in vacuum. To fully utilise this technique the hyperfine interaction must be modelled based on atomic structure calculations. Atomic structure calculations were performed using the most recent release of the General Relativistic Atomic Structure Package, and Monte-Carlo simulations of atomic-decay cascades in highly charged ions were developed. The simulations were used to fit experimental data on excited56Fe ions recoiling in vacuum with a view to determining the first-excited state g factor, g(21+), of56Fe.

Identification of EUV spectral profiles of laser-produced Cr plasmas

SynopsisLaser-produced chromium (Cr) plasmas have been measured by using a temporal-spatially resolved laser-produced plasma emission spectroscopy technique. The emission peaks in the wavelength range of 6.5-15 nm were identified from the 3p-4d, 5d, and 3p-4s transition lines from Cr5+ to Cr10+ ions with aid of Cowan and Flexible Atomic Code (FAC) atomic structure calculations, and through comparative analysis between experimental and simulated spectra.

Bayesian atomic structure calculations for collisional problems

SynopsisThe calculations of collisional processes require an accurate description of the target. In general, the atomic structure is obtained through tedious iterations in which a variety of configurations and parameters are chosen to minimize the differences between the numerical and experimental values of the energies and the oscillator strengths. Using a Bayesian machine learning analysis through a Tree–structured Parzen Estimator, we can reproduce the experimental atomic structure with high accuracy. Results for neutral beryllium are presented.

Investigation of temporal-resolved spectra of laser-produced titanium plasmas

SynopsisLaser-produced titanium (Ti) plasmas have been measured using temporal-spatially resolved laser-produced plasma emission spectroscopy technique. The emission peaks in the wavelength range of 7.5-15 nm were identified from the 3s-(4,5)p, 3p-4d, and 3d-4f transition lines from Ti5+ to Ti11+ ions with aid of NIST database and Cowan atomic structure calculations, as well as comparative analysis between experimental and simulated spectra based on a simplified radiation hydrodynamic model.

Soft x-ray emission from laser-produced strontium ions

Soft x-ray spectra, in the range from 2 nm to 9 nm, were recorded from strontium plasmas formed by pulses from 20 ps, 170 ps and 5.5 ns Nd:YAG lasers operating at the fundamental wavelength of 1064 nm. Features due to 3d–4p and 3d–4f transitions were identified by comparison with spectra from adjacent ions and atomic structure calculations with both the Cowan code and the Flexible Atomic Code. As in the spectra of ions of other elements in the fifth row of the periodic table, resonant lines 3dn–3dn−14p1, 3dn–3dn−14f1 and satellite lines 3dn−14s1–3dn−24s14p1, 3dn−14s1–3dn−24s14f1 of Δn = 1 were observed over the 3.0–8.5 nm region, emitted by 10+ to 19+ ions. These Δn = 1 transitions provide a range of narrow band emission features which may match to specific multi layer combinations for reflective optics in the extreme ultraviolet region of the spectrum.

Spectral characterization of an industrial EUV light source for nanolithography

The emission spectra from an industrial, droplet-based, laser-produced plasma, extreme ultraviolet light source for nanolithography are here presented and analyzed. The dependence of spectral features on the CO2-drive-laser intensity is studied by changing the beam spot size at constant pulse energy and duration. We characterize the spectrum by fitting the results of atomic structure calculations to the short-wavelength region (7–11 nm), where the contributions from various charge states can be resolved, and obtain the relative contributions of charge states Sn9+ –Sn15+ . These relative contributions are compared to charge state populations as calculated with the non-equilibrium plasma kinetics code flychk. The calculations are shown to be in good qualitative agreement with the results, showing that the effective plasma temperature, and with it, the shape of the unresolved, main emission feature at 13.5 nm, is a remarkably weak function of laser intensity under this source normal operating conditions.

Isotope-shift spectroscopy of the 1 S 0 → 3 P 1 and 1 S 0 → 3 P 0 transitions in strontium.

Isotope-shift spectroscopy with narrow optical transitions provides a benchmark for atomic structure calculations and has also been proposed as a way to constrain theories predicting physics beyond the standard model. Here we measure frequency shifts of the 1 S 0 → 3 P 1 and 1 S 0 → 3 P 0 transitions between 84Sr,86Sr, and 87Sr, relative to 88Sr. Using the isotope-shift measurements of the two transitions, a King plot analysis is performed, revealing a nonlinearity in the measured values.

Population of the states in collisions of mixed‐state (1s21S,1s2s3S) B3+ and C4+ ion beams with He and H2 targets

Auger KLn lines are observed in high‐resolution electron spectra obtained in collisions of mixed‐state (1s21S,1s2s3S) He‐like beams of 4 MeV B3+ with H2 and 6 MeV C4+ with He targets. Supporting atomic structure calculations show these lines to correspond to doubly excited states, which can be readily populated by electron transfer to the component of the mixed‐state beam. They thus provide indirect evidence for the existence of the corresponding KLn quartet states, similarly produced, even though their weak Auger decay does not allow for their direct observation in the electron spectra. These KLn quartet states mostly decay in a cascade chain of strong radiative E1 transitions, eventually terminating at the state, which is thus additionally enhanced. An upper limit on the state population due to cascades is obtained by assuming a statistical production of KLn quartet to doublet states followed by a 100% cascade feeding of the state. Our estimated upper limit is supported by our absolute cross section measurements and corresponding three‐electron atomic orbital close coupling calculations in progress. Results to date are presented and discussed.

Energies, electric dipole (E1), quadrupole (E2), octupole (E3) and magnetic dipole (M1), quadrupole (M2) transition rates for Ca XII, Ti XIV, Cr XVI, Fe XVIII and Ni XX

Energies, weighted oscillator strengths (gf), line strengths (S) and radiative rates (A) for allowed and forbidden transitions are presented for 2s2p62S1/2 − 2s22p52P1/2, 2P3/2 and 2s22p52P1/2 − 2s22p52P3/2 transitions in fluorine-like Ca XII (Z = 20), Ti XIV (Z = 22), Cr XVI (Z = 24), Fe XVIII (Z = 26) and Ni XX (Z = 28) ions. Moreover, the allowed electric dipole (E1) and the forbidden electric quadrupole (E2), octupole (E3), magnetic dipole (M1) and quadrupole (M2) transition rates for some transitions are obtained. The 2s22p5–2s 2p6-type transitions of F-like ions are prominent in high-temperature plasmas and are useful for diagnostics. The present results are obtained from configuration interaction atomic structure calculations using the code SUPERSTRUCTURE (SS) which includes relativistic effects in Breit–Pauli approximation. The comparison of the present energies with the available observed energies displayed very good agreement (< 1%). The presented excitation energy results have been compared with other detailed relativistic approaches such as Dirac–Fock, coupled cluster and configuration interaction for a few ionic states.

Lifetime measurements of ultrashort‐lived excited states in Be‐like ions

We propose to measure the lifetime of short‐lived excited states in highly charged ions by pump‐probe experiments. Utilizing two synchronized and delayed Femtosecond pulses allows accessing these lifetimes with Femtosecond precision. Such measurements could provide sensitive tests of state‐of‐the art atomic structure calculations beyond the capabilities of established methods.

K‐line X‐ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions

In the present work, we report an investigation of plasma environment effects on the atomic parameters associated with the K‐vacancy states in highly charged iron ions within the astrophysical context of accretion disks around black holes. More particularly, the sensitivity of K‐line X‐ray fluorescence parameters (wavelengths, radiative transition probabilities, and Auger rates) in Fe XVII–Fe XXV ions has been estimated for plasma conditions characterized by an electron temperature ranging from 105 to 107 K and an electron density ranging from 1018 to 1022 cm−3. In order to do this, relativistic multiconfiguration Dirac‐Fock atomic structure calculations have been carried out by considering a time averaged Debye‐Hückel potential for both the electron–nucleus and electron–electron interactions.