This manuscript is devoted to explore the atomic structure and electron impact excitation process of atom impurities in quantum dots. To achieve this goal, a method that solves the fully relativistic Dirac equation within the framework of relativistic configuration interaction is proposed. The Gaussian potential is used, which can accurately describe the location of impurities in quantum dots and their local effects on the surrounding electron cloud. The coupled Dirac equation is modified to include a new central potential, providing solutions that include both the continuous and bound state wave functions. The process of electron impact excitation is elucidated using the distorted wave method, all within the framework of relativistic Dirac theory. For illustrative purposes, a detailed investigation of the excitation energies, transition rates, wave functions, and excitation cross sections is carried out for a wide range of confinement strengths of the potential and quantum dot radii, using the helium impurities in spherical quantum dots as an example. Our results reveal that for a given confinement strength of the potential, the bound state wave functions are initially pulled into the inner region by the attractive Gaussian potential well, but eventually reflect the free atom scenario at large quantum dot radii. In contrast, the continuous electron wave functions exhibit monotonic variations as a function of the quantum dot radii. Such behavior of the wave functions gives rise to distinctive phenomena in the variation of excitation energies, transition rates, and excitation cross sections in relation to the potential parameters. Good agreement between the present results and existing data, where available, is obtained. This work holds importance not only for basic research in atomic physics but also for the optical and electronic applications of quantum dots. I.e., in the design and optimization of quantum dot lasers and quantum dot sensors.

Large-scale relativistic multiconfiguration Dirac-Fock calculations of energy levels and lifetimes of the 206 states arising from the 3s 2 3p, 3p 3 , 3s3p3d, 3p3d 2 , 3s 2 4p, 3s 2 4f, 3s3p 2 , 3s 2 3d, 3s3d 2 , 3s 2 4d, 3s 2 4s, 3s3p4s, 3s3p4d, 3p 2 3d, 3d 3 , and 3s3p4p configurations of Zr XXVIII, Nb XXIX, and Tc XXXI of tokamak interest are carried out. The active space approximation is employed for the calculations. To obtain accurate and convergent results, the calculations take into account the valence and core -valence correlations within the n = 9 complex, as well as the Breit interaction, self -energy corrections, and vacuum polarization corrections. Detailed information regarding the decay properties of these ions is provided, including the transition wavelengths, line strengths, and radiative transition rates for various types (electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions) of transitions among the levels of the aforementioned configurations. The uncertainties of each dipole transition are evaluated. The present data sets are compared to previous results and a good agreement is observed, which is valuable for emission line identification and fusion modeling, especially in situations where experimental data are scarce.

This manuscript provides a description of a relativistic method for calculating the atomic structure and photoionization process in the semiclassical dense electron-ion plasma environment. The method uses the effective interaction pseudo-potential derived for general two interacting charged particles taking into account the quantum mechanical and screening effects to model the strongly coupled effects. The results for (bound state) energies are obtained by numerically solving the Dirac equation. The present method uses the relativistic distorted-wave approach to calculate the continuum orbitals and the ionization cross sections by photon collision. The strongly coupled semiclassical plasma effects and the plasma ion shielding effects on various properties such as ionization energies, transition rates, and photoionization cross sections are studied, focusing on the hydrogen atom as a case study. Our results are in agreement with other theoretical data. This study has important implications for the fields of atomic physics, plasma physics, astrophysics, and fusion science, and provides valuable insights into the study of various scientific phenomena.

We describe a theoretical approach to calculate the electron impact dynamics of atoms/ions placed in a dense plasma. The model takes into consideration that the continuous electron and the guest atom/ion are affected by a recently proposed (dense) plasma shielding parameter potential. As a test case, the present numerical method is employed to study the electron-impact excitation of He-like Ti XXI by using the distorted-wave wavefunction in the framework of the fully relativistic theory. The finite temperature and density effects as well as solid density plasma effects on the excitation energies, transition properties, and integrated cross sections are discussed in detail, which shed light on the shielding parameter potential in resolving practical problems. Results are compared with the available measurements and previous computations. The present work is not only providing a new implementation of the finite-temperature method by a self-consistent methodology, but also of great interest for the high energy density physics community, i.e., our results are of interest to the fusion researches.

Elastic scattering of electrons on a finite-temperature quantum screened potential is studied by using the partial wave decomposition of scattering wavefunction. The influence of plasma temperature on the total and l = 0, 1, and 2 partial wave cross sections is systematically analyzed in the present work. It is found that when the plasma density is fixed, the screened strength does not change monotonically with temperature, which leads to different conditions for forming shape resonance in the scattering cross sections for the different temperature domains. The scattering cross sections under the environments of low temperature limit are compared with those for zero-temperature quantum plasmas.

Two kinds of novel methods, i.e., a self-consistent fully relativistic model and an analytical variational method based on the tensor expression of the Breit-Pauli Hamiltonian, are proposed to study the plasma effect on the atomic structure and photoionization dynamic process. The analytical plasma screening potential is used to reproduce a hot dense plasma environment. The self-consistent model incorporates the relativistic effect in the Dirac Hamiltonian. As to the variational method, the spin orbit splitting, relativistic mass correction and Darwin terms are included as perturbations. As an application, energy eigenvalues, transition energies, spectral line shifts, and photoionization cross sections of H-like Mg^11+ and Ni^27+ ions in a dense plasma environment are analyzed at selected temperatures and densities. A comparison between the present two sets of results is made. The present study not only helps us to understand the atomic structure and transition dynamics in plasma environments, but also provides an accurate data support for the diagnosis and analysis of plasma environments.

A method within the relativistic computational scheme is developed and used to investigate the electronic structures and spectra properties of plasma-embedded atoms/ions placed in an external electric-field by using the configuration interaction approximation, which is proved to be a powerful tool to include both the electron correlation and relativistic effect. In this scheme, the screening potential based on the self-consistent-field ion-sphere model is used to explain the effect of the plasma environment and the weak electric-field is considered as the external perturbation. As a first application, plasma-embedded He $$^{+}$$ ion is considered as an illustrative case. The influences of the different plasma temperature and density parameters and the external electric field strengths on the energy eigenvalues and transition properties are investigated in detail. Our results indicate that, inclusion of the screening effects destabilizes the atomic system (decreases energy eigenvalues and transition properties), whereas inclusion of the external electric field counteracts these effects by lowering the energies of the embedded case, thereby improving the stability of atomic system. Overall, compared to the electric field effect on the electronic structures and spectra properties of a guest ion, an obvious deflection takes place for the plasma screening, which implies that the latter has stronger effects. The present results are consistent with the results of the other available theoretical simulations.

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

Relativistic photoionization processes of an exemplary highly charged H-like ion Ar17+ for 1s1/2, 2lj (l = 0, 1), and 3lj (l = 1, 2) initial states are studied in plasmas with coulomb coupling parameter 0.007 < Γ < 0.202. Photoionization cross sections for both the strongly and weakly screened cases exhibit specific properties when their plasma densities and temperatures in the vicinities of the critical values at which nlj bound states enter the continuum. The electron degeneracy, finite-temperature gradient corrections, and quantum exchange-correlations effects have been included in the interaction between charged particles by the screened potential used in the present work. It is found that these effects for the plasmas with different coupled strength are reflected in the resonant regions of photoionization cross sections by comparing with Debye cases. The present work is expected to provide theoretical and data support for the fusion plasmas.

We propose a novel relativistic method to explore the atomic structure of highly charged ions perturbed by a dense plasma. The calculations are performed within the general framework of the ion sphere theory and application of the generalized analytical b-potential combined with the multi-configuration DiracFock approximation. In the method, the relativistic effects provided by the Dirac-Coulomb Hamiltonian, Breit interaction and two kinds of quantum electrodynamics corrections, self-energy and vacuum polarization, are accounted for systematically via perturbation theory. The level delocalizations, line shifts and radiative properties among the levels of the 2s(x)2p(y) (x + y = 5) configurations of Ni XXII under the finite temperature dense plasma conditions are demonstrated for illustrative purposes. Such ions can exist in inertial confinement devices or in laser-produced plasmas. Systematic changes are determined for the properties under study in respect of increased temperature and electron density. The obtained atomic structure, line shift, and level delocalization are essential fundamental properties for advanced diagnostics, equation of state calculations, line identifications, and benchmark data for ionization balance calculations ect. (C) 2021 Elsevier Ltd. All rights reserved.

The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction methods are used to provide excitation energies, lifetimes, and radiative transition data for the 604 (699, 702, 704, 704, 704, and 699) lowest levels of the 3s 23p 2, 3s3p 3, 3s 23p3d, 3p 4, 3s3p 23d, 3s 23d 2, 3p 33d, 3s3p3d 2, 3s3d 3, 3p3d 3, 3p 23d 2, 3s 23p4s, 3s 23p4p, 3s 23p4d, 3s 23p4f, 3s3p 24s, 3s3p 24p, 3s3p 24d, 3s3p 24f, 3s 23d4s, 3s 23d4p, 3p 34s, 3p 34p, 3s3p3d4s, 3s 23p5s, and 3s 23p5p configurations in Cr xi, (Mn xii, Fe xiii, Co xiv, Ni xv, Cu xvi, and Zn xvii). Previous line identifications of Fe xiii and Ni xv in the EUV and X-ray wavelength ranges are reviewed by comprehensively comparing the MCDHF theoretical results with available experimental data. Many recent identifications of Fe xiii and Ni xv lines are confirmed, and several new identifications for these two ions are proposed. A consistent atomic data set with spectroscopic accuracy is provided for the lowest hundreds of levels for Si-like ions of iron-group elements of astrophysical interest, for which experimental values are scarce. The uncertainty estimation method suggested by Kramida, applied to the comparison of the length and velocity line strength values, is used for ranking the transition data. The correlation of the latter with the gauge dependency patterns of the line strengths is investigated.

The relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method has been employed to calculate the atomic parameters of Mo XVIII, which are important for fusion determination of plasma properties in different conditions. Atomic data, such as energy levels, lifetimes, wavelengths, spectroscopic labels, and transition rates for the transitions among the lowest 112 states of the 3 s23p63d7, 3 s23p53d8, 3s3 p63d8, and 3s23p63d64s configurations are given. To describe the atomic system accurately, electron correlation effects are taken into account. We also present a calculation within fully relativistic frame based on the Flexible Atomic Code (FAC). This, in turn, allowed us to make an intercomparison on the obtained data. Our two sets of results are also evaluated by comparison with the NIST database recommended values. The new calculated energy levels are, on the average, about 1.5% higher than NIST database recommended values and yield oscillator strengths within 5% of the theoretical values. This study provides a substantial amount of updated atomic data, which are essential for fusion applications.

A method of analytically calculating energy levels of He-like ions in an environment of dense plasma is given by using the angular momentum coupling theory and irreducible tensor theory under Hartree–Fock approximation. In order to obtain higher calculation precision, relativistic correction terms of the non-relativistic energy including corrections caused by relativistic mass, one- and two-body Darwin effect, spin–spin contact interaction and orbit–orbit interaction, are calculated. The binding energies of the ground state $$1s^2$$ $$^1S$$ and excited state 1snp $$^1P$$ (n = 1 − 4) of He-like Cl ions and the transition energy between two energy levels in an environment of dense plasma are calculated. The scaling relationship between the energy shift of plasma and its temperature and density is given. According to our study, the energy shift of plasma conforms very well with the recent high-precision experimental result (Phys Rev A 100:012511, 2019).

In this paper, a new relativistic distorted wave approximation for cross section describing longitudinally-polarized electron impact excitation of ions in the presence of a strongly coupled plasma is proposed and implemented based on the flexible atomic code. The uniform electron gas model is used to incorporate the plasma effects, which includes the effect of static plasma screening on nuclear charge and the effect of confinement due to the neighbouring ions. For the bound and continuum wavefunctions, the Dirac equation with the ion-sphere potential is solved to account for relativistic effects. In order to check the consistency of the modifications, a self consistent theoretical attempt using the multiconfiguration Dirac-Fock method is also carried out to get the energy levels accounting for the plasma environment within the ion-sphere model. For the collision dynamics, as examples of applications, we investigate the total cross sections, the magnetic sublevels cross sections, and the degrees of circular polarizations of fluorescence radiation after 1s2 s01 →1s2s s03 and 1s2 s01 →1s2p p13,1 excitations of Helium-like Fe XXV ion by longitudinally-polarized electron impact with the ion-sphere potential. It is shown that the behavior of the cross sections for a pure Coulomb potential changes rapidly due to the plasma screening effects described by the ion-sphere potential in the process of calculating scattering matrix elements. A detailed, quantitative, comparison between the present results and other available theoretical values is presented for the plasma-free cases, showing good agreement. Our results contribute to a better understanding of the fundamentals of fluorescence polarization in strongly coupled plasmas. Results obtained in this work are beneficial for the diagnostic determination of laboratory plasmas.

We have performed the theoretical calculations of wavelengths and excitation energies from ground state for 56 fine-structure levels as well as of oscillator strengths and radiative decay rates for all the electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels of the terms belonging to the \(3s^{2}3p^{2}\), \(3s^{2}3p3d\), \(3s3p^{3}\), \(3s3p^{2}3d\), \(3s^{2}3d^{2}\), and \(3p^{4}\) configurations for the silicon isoelectronic sequence Cd XXXV-Ba XLIII, W LXI. The calculation is based on the multiconfiguration Dirac–Fock approach, and Breit interaction and quantum electrodynamic corrections are included. Electron correlation effects are taken into account by means of the expansions in terms of a basis of configuration state functions. To achieve the accuracy of the data, independent calculation is provided with similar data obtained from the flexible atomic code, taking W LXI as an example. Our results are compared with each other, and other available theories/experimental values and the energy levels/transition rates for a majority of strong transitions are found to be accurate to be better than 0.5%/10%. The present atomic data should be useful in controlled thermonuclear fusion research and technical plasma modeling.

Using fully relativistic multiconfiguration Dirac-Fock (MCDF) wavefunctions in the active space approximation, the energy levels, lifetimes, radiative rates, and oscillator strengths are determined for transitions in Mn-like W L ion. For the calculations, Breit interaction (BI) and quantum electrodynamics (QED) corrections to the levels are estimated in extensive relativistic configuration interaction (RCI) procedure, and results are reported for all electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the lowest 121 levels, belonging to the 3s(2)3 p(6)3d(7), 3s(2)3 p(5)3d(8), 3s3 p(6)3d(8), 3s(2)3 p(4)3d(9), and 3s3 p(5)3d(9) configurations. Comparisons are made with similar data obtained with FAC (Flexible Atomic Code) to assess the accuracy of the results. The present results are also assessed by comparison with the data compiled by the Atomic Spectra Database (ASD) of National Institute of Standards and Technology (NIST) and other existing theoretical/experimental ones for few levels in literature showing an overall good agreement. i.e., the energies agree within 0.5% with the experimental results, and the M1 transition rates agree within 5% with other theoretical results. Beside the ground configuration, almost all atomic parameters presented in this work are calculated for the first time and thus significantly increases the amount of accurate data for W L ion. Our results should be beneficial in future for identification of spectral lines, in plasma modelling, and in fusion plasma research.

We present results of accurate fully-relativistic calculations of transition energies and oscillator strengths among the levels of the 2s(2)2p(3), 2s2p(4), and 2p(5) configurations of N-like iron under dense plasma conditions, i.e., 19 times ionized atom of iron. Such highly-ionized species can exist in very hot plasmas, such as in cores of magneticfusion reactors, in X-ray free electron laser experiments and in imploaded targets of inertially-confined fusion (ICF) experiments. The ion sphere potential experienced by the electron is parameterized by temperature and electron density. Two independent atomic structure methods, namely the multiconfiguration Dirac-Hartree-Fock method and the flexible atomic code (FAC) representing the plasma shieldings with an average-atom ion-sphere (AAIS) potential and a uniform electron gas model (UEGM) potential, have been developed. The plasma-free values obtained in this work compare well with existing data from literature. Our results show that the levels of all studied configurations shift with the increase in plasma electron density, the shift of the 2s(2)2p(3) energies being negative and the shift of 2s2p(4) and 2p(5) positive. Moreover, the energy shift becomes more sensitive to the plasma electron density when the plasma electron temperature is lower. The oscillator strengths of the lines increase with the increase of electron density for a given temperature. The present results should be useful in fusion related plasmas and fundamental physics.

Using the fully relativistic distorted-wave method, we calculated electron impact excitation cross sections out of the two metastable levels of 4p^5 5 s J = 0 and J = 2 into the ten levels of the 4p^5 5p configuration of krypton. To obtain accurate results, careful consideration is given to the generation of the target state wave functions through the systematic inclusion of electron correlations. We find that the electron correlation has a large influence on the cross sections. This effect weakens as the incident electron energy increases. Our numerical results are compared with the available experimental data and other theoretical values over the measured energy range, showing a good quantitative agreement. We believe that these accurate results will be useful in plasma modeling studies.

Using the fully relativistic distorted-wave method, we calculated electron impact excitation cross sections out of the two metastable levels of $$4p^{5}$$ 5sJ = 0 and J = 2 into the ten levels of the $$4p^{5}$$ 5p configuration of krypton. To obtain accurate results, careful consideration is given to the generation of the target state wave functions through the systematic inclusion of electron correlations. We find that the electron correlation has a large influence on the cross sections. This effect weakens as the incident electron energy increases. Our numerical results are compared with the available experimental data and other theoretical values over the measured energy range, showing a good quantitative agreement. We believe that these accurate results will be useful in plasma modeling studies.

Investigations on the energies and radiative properties of a highly charged ion embedded in plasma in the weak-and strong-coupling regimes are made, taking the Al9+ ion as an example. The Debye and ion-sphere (IS) potentials are adopted to describe the plasma screening effects, respectively. The multiconfiguration Dirac-Fock (MCDF) method is employed to describe the relativistic and electronic correlation effects in the above atomic system. The screening effects on the ionization potential (IP), transition energies, and radiative rates are estimated. Results obtained are compared with the available results in the literature. Comparisons between the Debye and IS models results are also carried out considering similar plasma conditions. The present data are useful for diagnostics of astrophysical and laboratory plasmas.