Search Results (44)

We present high-precision multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for the metastable states of ${\mathrm{Pr}}^{9+}$ and ${\mathrm{Nd}}^{10+}$ ions, systematically investigating their energy levels, transition properties, Landé $g_J$ factors, and hyperfine interaction constants. Our results show excellent agreement with available experimental data and theoretical benchmarks, while resolving critical configuration assignment discrepancies through detailed angular momentum coupling analysis. The calculations highlight the significant role of Breit interaction and provide the first theoretical predictions of electric quadrupole hyperfine constants ($B_{\mathrm{hfs}}$). These findings deliver essential atomic data for the development of next-generation optical clocks and establish lanthanide highly charged ions as exceptional candidates for precision tests of fundamental physics. Full article

We present excitation energies, transition wavelengths, electric dipole (E1) transition rates, oscillator strengths, line strengths, and lifetimes for the 86 lowest states up to and including $1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}7\mathrm{f}$ in N iii, the 125 lowest states up to and including $1{\mathrm{s}}^{2}2\mathrm{s}7\mathrm{f}$ in N iv, and the 53 lowest states up to $1{\mathrm{s}}^{2}8\mathrm{g}$ in N v using the multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods. The computed results are then compared with data from the Atomic Spectra Database of the National Institute of Standards and Technology (NIST-ASD), experimental results, and other theoretical studies. For all levels in N iii – v, the root mean square energy differences from the NIST values are 130, 103, and 6 cm⁻¹, respectively. Compared to previous multiconfiguration Hartree–Fock and the Breit–Pauli (MCHF-BP) calculations, 89.3%, 98.5%, and 100% of the $log\left(gf\right)$ values for N iii – v agree within 5%, respectively. Full article

This article presents the maiden investigation of the electronic structural properties of the Sr⁺ ion confined inside fullerene. The Dirac equations are solved to calculate the energy levels, probability distributions, etc. for various confinement depths of the Gaussian Annular Square Well (GASW) potential using the Multi-Configuration Dirac Hartree–Fock (MCDHF) formalism. The wavelengths, transition probabilities, and oscillator strengths are reported for the $5S_{1/2}⟷5P_{1/2}$ ($D_1$ line) and $5S_{1/2}⟷5P_{3/2}$ ($D_2$ line) transitions of the encapsulated ion. We also estimate variations in the line intensity ratio, electron density, Coulomb coupling parameter, etc. A suggested direction for the calculation of electron impact ionization cross-section using the binary-encounter Bethe (BEB) model with the present data is also given. Full article

The multi-configurational Dirac–Hartree–Fock method has been used to examine the electron correlation effect on wavelengths and transition rates for $L\to K$ transitions occurring in He- and Li-like nickel ions. The collisional-radiative modelling approach has been used to simulate the X-ray spectra, in a 1.585–1.620 Å wavelength range, originating from the He-like nickel ions and their dielectronic Li-, Be-, and B-like satellites for various electron temperature values in the 2 keV to 8 keV range. The presented results may be useful in improving the plasma electron temperature diagnostics based on nickel spectra. Full article

In this work, we present a new set of transition probabilities for experimentally classified spectral lines in the Os VI spectrum. To do this, two independent computational approaches based on the pseudo-relativistic Hartree–Fock, including core polarization effects (HFR+CPOL) and fully relativistic Multiconfiguration Dirac–Hartree–Fock (MCDHF) methods, were used, with the detailed comparison of the results obtained with these two approaches allowing us to estimate the quality of the calculated radiative parameters. These atomic data, corresponding to 367 lines of five-times ionized osmium between 438.720 and 1486.275 Å, are expected to be useful for the analysis of the spectra emitted by fusion plasmas in which osmium could appear as a result of transmutation by the neutron bombardment of tungsten used as component of the reactor wall, such as the ITER divertor. Full article

Corrections to the measured nuclear magnetic moments obtained from hyperfine structure measurements include the Breit–Rosenthal effect. In this paper, we present results from calculations on Bi using the GRASP2018 code. The results indicate that the Breit–Rosenthal effect is on the order of 0.1$\%{\mathrm{fm}}^{-2}$, the same order of magnitude as neighbouring elements, while some atomic states may have one order of magnitude smaller values. The ground state $6p^3 {}^{4}S_{3/2}^o$ is more sensitive to the Breit–Rosenthal effect, and hence the hyperfine anomaly, with a value of −0.25$\%{\mathrm{fm}}^{-2}$. Full article

This work presents ab initio calculations for the K$\alpha$ spectrum of manganese (Z = 25, [Ar]$3d^{5}4s^2$), a highly complex system due to the five open orbitals in the $3d$ shell. The spectrum is composed of the canonical diagram line $\left[1s\right]\to \left[2p\right]$ and shake-off satellite lines $\left[1snl\right]\to \left[2pnl\right]$ ($nl\in \{2s,2p,3s,3p,3d,4s\}$), where square brackets denote a hole state. The multiconfiguration Dirac–Hartree–Fock method with the active set approach provides the initial and final atomic wavefunctions. Results are presented as energy eigenvalue spectra for the diagram and satellite transitions. The calculated wavefunctions include over one hundred million configuration state functions and over 280,000 independent transition energies for the seven sets of spectra considered. Shake-off probabilities and Auger transition rates determine satellite intensities. The number of configuration state functions ensures highly-converged wavefunctions. Several measures of convergence demonstrate convergence in the calculated parameters. We obtain convergence of the transition energies in all eight transitions to within 0.06 eV and shake-off probabilities to within 4.5%. Full article

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the $\{2s^{2}2p^3,2s^{2}2p^{2}3p,2s^{2}2p^{2}4p\}$ odd and $\{2s^{2}2p^{2}3s,2s2p^4,2s^{2}2p^{2}4s,2s^{2}2p^{2}3d\}$ even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the $1s$ and $2s$ core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the $2s^{2}2p^{2}3s$ configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations. Full article

In this paper, we update the phase-space factors for all two-neutrino double electron capture processes. The Dirac–Hartree–Fock–Slater self-consistent method is employed to describe the bound states of captured electrons, enabling a more realistic treatment of atomic screening and more precise binding energies of the captured electrons compared to previous investigations. Additionally, we consider all s-wave electrons available for capture, expanding beyond the K and $L_1$ orbitals considered in prior studies. For light atoms, the increase associated with additional captures compensates for the decrease in decay rate caused by the more precise atomic screening. However, for medium and heavy atoms, an increase in the decay rate, up to 10% for the heaviest atoms, is observed due to the combination of these two effects. In the systematic analysis, we also include capture fractions for the first few dominant partial captures. Our precise model enables a close examination of low Q-value double electron capture in ¹⁵²Gd, ¹⁶⁴Er, and ²⁴²Cm, where partial $KK$ captures are energetically forbidden. Finally, with the updated phase-space values, we recalculate the effective nuclear matrix elements and compare their spread with those associated with $2\nu {\beta }^{-}{\beta }^{-}$ decay. Full article

Recent advancements in studying long chains of unstable nuclei have revitalised interest in investigating the hyperfine anomaly. Hyperfine anomaly is particularly relevant for determining nuclear magnetic dipole moments using hyperfine structures where it limits the accuracy. This research paper focuses on the calculation of the differential Breit-Rosenthal effect for the $6p^2{}^3{P}_{1,2}$, ${}^1{D}_2$ and $6p7s{}^3{P}_1$ states in Pb, utilising the multi-configurational Dirac-Hartree-Fock code, GRASP2018. The findings show that the differential Breit-Rosenthal effect is typically less than $0.1/\mathrm{f}{\mathrm{m}}^2$, which is often much smaller than the Bohr-Weisskopf effect. The differential Breit-Rosenthal effect for the $6p^2{}^3{P}_2$ state is one order of magnitude smaller than the rest, which is why this state seems to be insensible to the hyperfine anomaly. Full article

In this work, a krypton gas impurity seeding experiment was conducted in a Large Helical Device. Emission lines from the Na-like Kr ion in the extreme ultraviolet wavelength region, such as 22.00 nm, 17.89 nm, 16.51 nm, 15.99 nm, and 14.08 nm, respective to $2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{1/2}^{\mathrm{o}})-2{\mathrm{p}}^{6}3\mathrm{s}{(}^2{\mathrm{S}}_{1/2})$, $2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{3/2}^{\mathrm{o}})-2{\mathrm{p}}^{6}3\mathrm{s}{(}^2{\mathrm{S}}_{1/2})$, $2{\mathrm{p}}^{6}3\mathrm{d}{(}^2{\mathrm{D}}_{3/2})-2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{3/2}^{\mathrm{o}})$, $2{\mathrm{p}}^{6}3\mathrm{d}{(}^2{\mathrm{D}}_{5/2})-2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{3/2}^{\mathrm{o}})$, and $2{\mathrm{p}}^{6}3\mathrm{d}{(}^2{\mathrm{D}}_{3/2})-2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{1/2}^{\mathrm{o}})$ transitions, are observed. In order to generate a theoretical synthetic spectrum, an extensive calculation concerning the excitation of the ${\mathrm{Kr}}^{25+}$ ion through electron impact was performed for the development of a suitable plasma model. For this, the relativistic multiconfiguration Dirac–Hartree–Fock method was employed along with its extension to the relativistic configuration interaction method to compute the relativistic bound-state wave functions and excitation energies of the fine structure levels using the General Relativistic Atomic Structure Package-2018. In addition, another set of calculations was carried out utilizing the relativistic many-body perturbation theory and relativistic configuration interaction methods integrated within the Flexible Atomic Code. To investigate the reliability of our findings, the results of excitation energies, transition probabilities, and weighted oscillator strengths of different dipole-allowed transitions obtained from these different methods are presented and compared with the available data. Further, the detailed electron impact excitation cross-sections and their respective rate coefficients are obtained for various fine structure resolved transitions using the fully relativistic distorted wave method. Rate coefficients, calculated using the Flexible Atomic Code for population and de-population kinetic processes, are integrated into the collisional-radiative plasma model to generate a theoretical spectrum. Further, the emission lines observed from the ${\mathrm{Kr}}^{25+}$ ion in the impurity seeding experiment were compared with the present plasma model spectrum, demonstrating a noteworthy overall agreement between the measurement and the theoretical synthetic spectrum. Full article

Ab initio calculations sometimes do not reproduce the experimentally observed energy separations at a high enough accuracy. Fine-tuning of diagonal elements of the Hamiltonian matrix is a process which seeks to ensure that calculated energy separations of the states that mix are in agreement with experiment. The process gives more accurate measures of the mixing than can be obtained in ab initio calculations. Fine-tuning requires the Hamiltonian matrix to be diagonally dominant, which is generally not the case for calculations based on $jj$-coupled configuration state functions. We show that this problem can be circumvented by a method that transforms the Hamiltonian in $jj$-coupling to a Hamiltonian in $LSJ$-coupling for which fine-tuning applies. The fine-tuned matrix is then transformed back to a Hamiltonian in $jj$-coupling. The implementation of the method into the General Relativistic Atomic Structure Package is described and test runs to validate the program operations are reported. The new method is applied to the computation of the $2s^2{}^1{S}_0-2s2p{}^{1,3}{P}_1$ transitions in C III and to the computation of Rydberg transitions in B I, for which the $2s2p^2{}^2{S}_{1/2}$ perturber enters the $2s^{2}ns{}^2{S}_{1/2}$ series. Improved convergence patterns and results are found compared with ab initio calculations. Full article

grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence. Full article

The latest published version of GRASP (General-purpose Relativistic Atomic Structure Package), i.e., GRASP2018, retains a few suboptimal subroutines/algorithms, which reflect the limited memory and file storage of computers available in the 1980s. Here we show how the efficiency of the relativistic self-consistent-field (SCF) procedure of the multiconfiguration-Dirac–Hartree–Fock (MCDHF) method and the relativistic configuration-interaction (RCI) calculations can be improved significantly. Compared with the original GRASP codes, the present modified version reduces the CPU times by factors of a few tens or more. The MPI performances for all the original and modified codes are carefully analyzed. Except for diagonalization, all computational processes show good MPI scaling. Full article

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes and isotope separators. A number of different computational methods, each with their own strengths and weaknesses, is available to meet these tasks. Here, we review the relativistic multiconfiguration method as it applies to the General Relativistic Atomic Structure Package [grasp2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, J. Bieroń, Comput. Phys. Commun. (2018). DOI: 10.1016/j.cpc.2018.10.032]. To illustrate the capacity of the package, examples of calculations of relevance for nuclear physics and astrophysics are presented. Full article