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The singlet S-wave resonances of the He atom embedded in dense quantum plasmas are investigated by applying the complex-coordinate rotation method. The modified Debye–Hückel potential is used to model the effective interactions of the test atom in a dense quantum plasma environment. The explicitly correlated Hylleraas configuration-interaction basis function is employed to take into account the electron correlation effect. The first ten S-wave resonance states of the He atom below the N = 2 thresholds of the He+ ion are calculated, and the resonance energies and widths at a variety of screening parameters are obtained with high accuracy. The plasma screening effect on the expectation values of the radial and angular physical quantities are analyzed for the first time. [ABSTRACT FROM AUTHOR]

The static multipole polarizabilities of the hydrogen atom interacting with a screened Coulomb potential confined in an impenetrable spherical box are calculated in the sum‐over‐states formalism. The system eigenenergies and wave functions are produced by employing the generalized pseudospectral method. High‐precision results are obtained to resolve the discrepancies between previous predictions, and used to analyze the critical behavior of the system with varying the confinement radius and screening parameter. A scaling law of the multipole polarizabilities with respect to the nuclear charge and electron reduced mass is proposed. Based on the scaling law we extend the investigation to the spatially confined positronium atom in a screened Coulomb potential by utilizing a reduced one‐electron model. The results are in good agreement with previous estimates. However, it is conjectured that when the confinement radius is small the confined positronium atom should be treated more reasonably by an effective two‐electron model. [ABSTRACT FROM AUTHOR]

The correct understanding of the behavior of highly stripped ions immersed in a dense plasma environment is a hitherto challenge for theory and it is of importance in various applications. Here, we developed four kinds of novel theoretical models to the determination of the spectral properties and collision dynamics of H‐like ions in dense and hot plasmas by employing the analytical potential [Li et al., Phys. Plasmas2019, 26, 033301] to describe the interactions among the charged particles: (i) The electron photon processes in plasma model within the relativistic scheme; (ii) The multiconfiguration Dirac–Fock model within the framework of relativistic self‐consistent iteration approximation; (iii) The generalized pseudospectral method within the relativistic framework; and (iv) An analytic formula based on the Hartree–Fock method and the irreducible tensor theory within the non‐relativistic regime, derived from a solution of Schrödinger equation. As a typical example, energy eigenvalues, radiative transition properties, spectral line shifts, and electron impact excitation and ionization cross sections of the selected N6+ and Ne9+ ions are determined for several temperature‐density cases, characteristic of inertial confinement fusion plasmas. A comparison of these results with each other and the results from earlier calculations as well as with the available experimental data is provided. Systematic trend is determined for all the properties under study concerning increased screening. The present study not only extends our understanding of the dense plasma shielding effects, but also opens the way for future investigations allowing accurate predictions of spectral properties of ions in dense and hot plasmas aimed at providing precision data for various practical applications. [ABSTRACT FROM AUTHOR]

The first‐order relativistic corrections to the non‐relativistic energies of hydrogen‐like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye–Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen‐like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin‐orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin‐orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativistic‐corrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first‐order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter. [ABSTRACT FROM AUTHOR]

The explicitly‐correlated basis sets are much easier to be linearly dependent than the product type bases constructed by one‐electron orbitals due to the explicit inclusion of interelectronic coordinates in system wave functions. In this work, we apply Löwdin's canonical orthogonalization method to study the linearly dependent problems arising from the variational calculations based on Hylleraas configuration‐interaction (Hy‐CI) basis functions. Both the ground and excited states of He atom are calculated with increasingly large basis sets. Our results show that the linear dependence in Hy‐CI basis sets can be successfully overcome by employing Löwdin's canonical orthogonalization method, yet without using extended higher‐precision arithmetic in numerical implementations. Therefore, the computational effort can be reduced considerably. It is expected that the present method can be applied to other types of explicitly correlated basis functions. [ABSTRACT FROM AUTHOR]