Collinear configuration of the helium atom and two-electron ions

Liverts, Evgeny Z.; Krivec, R.; Barnea, Nir

doi:10.1016/j.aop.2020.168306

Cited by 6 publications

(19 citation statements)

References 29 publications

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“…Unlike the previous studies we considered r as a quantum mechanical variable but not as a parameter. It is worth noting that the "electrons-on-sphere" and the "collinear" configuration [16] are coincident in two boundary points. For θ = 0 one obtains the state of the electron-electron coalescence, whereas the angle θ = π characterizes the e-n-e configuration when the electrons are located at the ends of the diameter of sphere with the nucleus at its center (see Fig.…”

Section: Discussionmentioning

confidence: 99%

“…In our previous article [16] the collinear configuration of the ground state of the twoelectron atom/ion was studied. The relevant collinear wave function (WF) K(r, λ) ≡ Ψ(r, |λ|r, (1 − λ)r) is the particular case of the general WF, Ψ with the collinear parameter λ ∈ [−1 , 1].…”

Section: The Ground-state Configuration Of the Helium-like Atom/ion P...mentioning

confidence: 99%

“…These are the nucleus charge Z and the non-relativistic energy E of the two-electron atom/ion (see, e.g., [28]). As to the coefficients c 2 and c 3 then it is important to note that the corresponding calculations include the extra parameter a 21 (see the Appendix) which has not been reliably calculated previously (see also [16]).…”

Section: The Fock Expansionmentioning

confidence: 99%

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Averaged electron densities of the helium-like atomic systems

Liverts

Krivec

2020

Journal of Mathematical Physics

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Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using the Pekeris-like method [2], the ground state wave functions Ψ of the heliumlike atoms with nucleus charge 1 ≤ Z ≤ 5 are calculated in a few coordinate systems including the hyperspherical coordinates {R, α, θ}. The wave functions Ψ av (R) of the hyperspherical radius R are calculated numerically by averaging Ψ over the hyperspherical angles α and θ. The exact analytic representations for the relative derivatives Ψ av (0)/Ψ av (0) and Ψ av (0)/Ψ av (0) are derived. Analytic approximations very close to the actual Ψ av (R) are obtained. Using actual wave functions Ψ, the one-electron densities ρ(r) are calculated as functions of the electron-nucleus distance r. The relevant derivatives ρ (0)/ρ(0) and ρ (0)/ρ(0) characterizing the behavior of ρ(r) near the nucleus are calculated numerically. Very accurate analytical approximations, representing the actual one-electron density both near the nucleus and far away from it, are derived. All the analytical and numerical results are supplemented with tables and graphs.

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Section: Discussionmentioning

confidence: 99%

Section: The Ground-state Configuration Of the Helium-like Atom/ion P...mentioning

confidence: 99%

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Averaged electron densities of the helium-like atomic systems

Liverts

Krivec

2020

Journal of Mathematical Physics

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“…As it was mentioned above, to obtain the fully defined model WF of the form (1) one needs to determine 2N coefficients. To solve the problem with given equations ( 10) and (11), we need to find extra 2(N − 1) coupled equations for parameters of the exponential form (1). To this end we propose to use the definite integral properties of the collinear WF…”

Section: Calculation Techniquementioning

confidence: 99%

“…In this paper we present a technique for building compact and simple wave functions of high accuracy, describing two-electron atomic systems such as H − , He, Li + , Be 2+ and B 3+ with the collinear arrangement of the particles [1]. The study of mechanism of double photoionization of the helium-like atomic systems by high energy photons [2,3] can serve as an example of possible application (see the details in the next Section).…”

Section: Introductionmentioning

confidence: 99%

Accurate exponential representations for the ground states of the collinear two-electron atomic systems

Liverts,

Barnea

2021

Preprint

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In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant S-state. It is worth noting that the considered states include the wellknown states of the electron-nucleus and electron-electron coalescences as a particular case. The simplicity and compactness imply that the considered wave functions represent a linear combinations of few single exponentials. We have calculated such model wave functions for the ground state of helium and the two-electron ions with nucleus charge 1 ≤ Z ≤ 5. The parameters and the accompanying characteristics of these functions are presented in tables for number of exponential from 3 to 6. The accuracy of the resulting wave functions are confirmed graphically. The specific properties of the relevant codes by Wolfram Mathematica are discussed. An example of application of the compact wave functions under consideration is reported.

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Co-spherical electronic configuration of the helium-like atomic systems

Liverts¹

2022

Annals of Physics

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Collinear configuration of the helium atom and two-electron ions

Cited by 6 publications

References 29 publications

Averaged electron densities of the helium-like atomic systems

Averaged electron densities of the helium-like atomic systems

Accurate exponential representations for the ground states of the collinear two-electron atomic systems

Co-spherical electronic configuration of the helium-like atomic systems

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