Atomic structure under external confinement: effect of plasma on the spin orbit splitting, relativistic mass correction and Darwin term for hydrogen-like ions

Chaudhuri, Supriya K.; Mukherjee, P. K.; Fricke, B.

doi:10.1140/epjd/e2017-70511-6

Cited by 19 publications

(9 citation statements)

References 36 publications

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“…The comparisons of E (0) , E m , and E D for all three types of SCP are demonstrated in Figure 5 for an overview. It is interestingly found that although our calculations on E (0) and E m are in good agreement with the predictions of Chaudhuri et al [56], the Darwin term E D , however, show opposite changes as varying the screening parameter. Similar situation is found on the Darwin term for all the ground states of H iso-electronic sequence with both SCP and ECSCP.…”

Section: Relativistic Correctionssupporting

confidence: 89%

“…Darwin term E D , and the spin-orbit coupling term E so , respectively. The more concrete form of these terms are given by [54,56]…”

Section: Relativistic Correctionsmentioning

confidence: 99%

“…For practical purposes, the fully relativistic calculations based on Dirac equation would shed more light on such critical phenomena. "a" and "b" refer to the calculations by Chaudhuri et al [56] and Poszwa [54], respectively. Numbers in parentheses represent the power of 10.…”

Section: Relativistic Correctionsmentioning

confidence: 99%

“…In the following discussion, we would like to take a detailed comparison with the predictions of Chaudhuri et al [56] who employed the basis-set expansion method based on Slater-type orbitals. The authors presented systematic investigations on individual relativistic correction terms for hydrogen-like ions with Z = 6-22, in both SCP and ECSCP.…”

Section: Relativistic Correctionsmentioning

confidence: 99%

“…The effectiveness of the direct perturbation theory is then confirmed by the same author [55] for hydrogen-like ions with nuclear charge up to 40, through a comparison with the fully relativistic calculations of the Dirac equation. The most recent work of Chaudhuri et al [56] solved the non-relativistic energies and the first-order relativistic corrections by expanding the system wave function in terms of Slater-type orbitals which, to the best of our knowledge, is the first investigation on the individual contribution of the three relativistic terms on atomic structure under screening confinements. The variations of relativistic mass correction, Darwin term, and spin-orbit splitting for the ground as well as the first two p-wave excited states of hydrogen-like ions (from C 5+ to Ti 21+ ) embedded in both SCP and ECSCP are provided for a wide range of screening parameters.…”

mentioning

confidence: 99%

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High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials

Xie

Jiao

Liu

et al. 2021

Int J of Quantum Chemistry

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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 relativisticcorrected 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.

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Section: Relativistic Correctionssupporting

confidence: 89%

“…Darwin term E D , and the spin-orbit coupling term E so , respectively. The more concrete form of these terms are given by [54,56]…”

Section: Relativistic Correctionsmentioning

confidence: 99%

Section: Relativistic Correctionsmentioning

confidence: 99%

Section: Relativistic Correctionsmentioning

confidence: 99%

mentioning

confidence: 99%

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High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials

Xie

Jiao

Liu

et al. 2021

Int J of Quantum Chemistry

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Revisiting the generalized pseudospectral method: Radial expectation values, fine structure, and hyperfine splitting of confined atom

Zhu

Jiao

et al. 2020

Int J of Quantum Chemistry

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This paper revisits the generalized pseudospectral (GPS) method on the calculation of various radial expectation values of atomic systems, especially on the spatially confined hydrogen atom and harmonic oscillator. As one of the collocation methods based on global functions, the powerfulness and robustness of the GPS method has been well established in solving the radial Schrödinger equation with high accuracy.However, in our recent work, it was found that the previous calculations based on the GPS method for the radial expectation values of confined systems show significant discrepancies with other theoretical methods. In this work we have tackled such a problem by tracing its source to the GPS method and found that the method itself may not be able to obtain the system wave function at the origin. Combined with an extrapolation method developed here, the GPS method can fully reproduce the radial quantities obtained by other theoretical methods, but with more flexibility, efficiency, and accuracy. We apply the GPS-extrapolation method to investigate the relatievistic fine structure and hyperfine splitting of confined hydrogen atom in s-wave states where the zero-point wave function dominates. Good agreement with previous predictions is obtained for confined hydrogen in low-lying states, and benchmark results are obtained for high-lying excited states. The perturbation treatment of the fine and hyperfine interactions is validated in the confining environment. K E Y W O R D Sconfined atom, fine structure, generalized pseudospectral method, hyperfine splitting, radial expectation value | INTRODUCTIONIn the past few years, the generalized pseudospectral (GPS) method, which is also known as the semispectral method or collocation method, has been successfully applied to investigate the structural properties of atomic and molecular systems, [1][2][3][4][5] the quantum scattering processes in nuclear and atomic physics, [6,7] and the laser-atom interactions. [8][9][10] Its usefulness has been continuously revealed in recent years in accurately and efficiently solving both the time-independent and time-dependent Schrödinger and Dirac equations. Being a type of discrete variable representation (DVR) method, the GPS method shows its special superiority over other generalizations of DVR, such as the finite difference and finite element methods. For example, the Numerov and Runge-Kutta methods, as in the latter case, are local approaches to the unknown function by a sequence of overlapping low-order polynomials in a small subset of user-defined grid points. [11,12] The GPS method and its variants in different forms are generally global approaches to the unknown function using global basis functions with a high degree, for example, the trigonometric

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Analytical Calculation of Cl$$^{15+}$$ Ion Immersed in Dense Plasmas

Chu

Chen

2020

Few-Body Syst

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Atomic structure under external confinement: effect of plasma on the spin orbit splitting, relativistic mass correction and Darwin term for hydrogen-like ions

Cited by 19 publications

References 36 publications

High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials

High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials

Revisiting the generalized pseudospectral method: Radial expectation values, fine structure, and hyperfine splitting of confined atom

Analytical Calculation of Cl$$^{15+}$$ Ion Immersed in Dense Plasmas

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