Finite element three-body studies of bound and resonant states in atoms and molecules

Alferova, T.; Andersson, Stefan; Elander, Nils; Levin, S. B.; Yarevsky, E. A.

doi:10.1016/s0065-3276(01)40023-2

Cited by 5 publications

(5 citation statements)

References 48 publications

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“…Therefore, Eq. ( 11) is suitable for ECS [5,6,13] with the exterior scaling radius Q ≥ R. After ECS, the function Φ becomes an exponentially decreasing function, implying that boundary conditions equal to zero can be used in order to solve the ECS-transformed equation (11).…”

Section: A Potential Splitting Approachmentioning

confidence: 99%

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Potential splitting approach to e–H and e–He⁺scattering

Yarevsky

Yakovlev

Elander

2017

J. Phys. B: At. Mol. Opt. Phys.

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An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schrödinger equation for the long range tail of the reaction potential is used as an incoming wave. This reformulation of the scattering problem into an inhomogeneous Schrödinger equation with asymptotic outgoing waves makes it suitable for solving with the exterior complex scaling technique. The validity of the approach is analyzed from a formal point of view and demonstrated numerically, where the calculations are performed with the finite element method. The method of splitting the potential in this way is illustrated with calculations of the electron scattering on the hydrogen atom and the positive helium ion in energy regions where resonances appear.

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Section: A Potential Splitting Approachmentioning

confidence: 99%

“…First, the ECS method with Q ≥ R is applied to the driven Eqs. (16,19) as discussed in [13,17]. In this method, each of the spatial coordinates is replaced with the complex one r → s φ (r), where φ is the asymptotic rotation angle.…”

Section: B Asymptotic Behaviour Of the Scattering Wave Functionmentioning

confidence: 99%

Potential splitting approach to e–H and e–He⁺scattering

Yarevsky

Yakovlev

Elander

2017

J. Phys. B: At. Mol. Opt. Phys.

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“…Furthermore, the method is feasible on parallel computers. Other references include [26,27], and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Finite‐element calculations for the helium atom

Zheng

Ying

2003

Int J of Quantum Chemistry

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ABSTRACT:We give the explicit form of the Hylleraas-Breit transform in the current paper and apply it to fixed-nucleus problems of heliumlike ions. Employing the relation between the total angular momentum and the Hamilton, the six-dimensional Schrö dinger equation is transferred into three-dimensional systems of equations. We use the Lagrange finite-element method to obtain numerical solutions for some lowlying S, 1s2p 3 P, and 1s3d 3 D states of the helium atom.

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“…Numerical techniques based on spline methods [20,21], finite element techniques [22][23][24][25], or global basis set techniques cannot in a simple manner be applicable to the techniques used by Rittby et al [18] and Krylstedt et al [19].…”

Section: Introductionmentioning

confidence: 99%

“…Recent numerical methods applied in complex dilation studies are especially designed to obtain resonant eigenvalues and eigenfunctions. Numerical techniques based on spline methods 20, 21, finite element techniques 22–25, or global basis set techniques cannot in a simple manner be applicable to the techniques used by Rittby et al 18 and Krylstedt et al 19.…”

Section: Introductionmentioning

confidence: 99%

S‐matrix expansions in view of complex dilation theories

Alferova

Elander

2002

Int J of Quantum Chemistry

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ABSTRACT:In this article, we use the complex dilation formalism to compute Smatrix residues for a number of complex Schrödinger-type eigenvalues in a limited spectral region. These residues are then used as expansion parameters for the corresponding S-matrix. The aim of this work is to find numerically stable algorithms that can be applied to problems based on realistic only numerically represented potentials. Two formalisms are described. In the first, we compute the Jost functions Ᏺ ϩ (k) and Ᏺ Ϫ (k) as well as the derivative dᏲ/dk numerically at the eigenvalue k . Using the second method, we generalize a formula described by Newton [(Scattering Theory of Waves and Particles; McGraw-Hill; New York, 1966) for bound states to resonant eigenvalues. Here, the S-matrix residue is obtained by integrating the resonant eigenfunction in the complex coordinate space. Our formalism is tested on an exactly solvable problem (Bargmann, V. Phys Rev 1949, 75, 301-303) and a classic complex dilation potential (Bain, R. A. et al.

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Finite element three-body studies of bound and resonant states in atoms and molecules

Cited by 5 publications

References 48 publications

Potential splitting approach to e–H and e–He⁺scattering

Potential splitting approach to e–H and e–He⁺scattering

Finite‐element calculations for the helium atom

S‐matrix expansions in view of complex dilation theories

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Finite element three-body studies of bound and resonant states in atoms and molecules

Cited by 5 publications

References 48 publications

Potential splitting approach to e–H and e–He+scattering

Potential splitting approach to e–H and e–He+scattering

Finite‐element calculations for the helium atom

S‐matrix expansions in view of complex dilation theories

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Potential splitting approach to e–H and e–He⁺scattering

Potential splitting approach to e–H and e–He⁺scattering