Exterior complex scaling method applied to doubly excited states of helium

Elander, Nils; Yarevsky, E. A.

doi:10.1103/physreva.57.3119

Cited by 47 publications

(43 citation statements)

References 17 publications

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“…The inclusion of increasingly diffuse Gaussians or expansively 1 3 2 5 4 # 6 0 6 8 72 @ 9 A B D C 7E @ 9 A B 2 @ F H G P I R Q A B S C 7E 5 9 T E @ U W V S F B # X G P I R Q A B S C 7E 5 large basis sets as a remedy to their locality eventually fails due to the development of linear dependencies within the Gaussian basis. Furthermore, in connection with exterior complex scaling, Gaussian functions, like other analytic basis functions, require a cumbersome "smoothed" exterior scaling treatment that can produce unwanted physical consequences [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Hybrid approach to molecular continuum processes combining Gaussian basis functions and the discrete variable representation

et al. 2005

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Gaussian basis functons, routinely employed in molecular electronic structure calculations, can be combined with numerical grid-based functions in a discrete variable representation to provide an efficient method for computing molecular continuum wave functions. This approach, combined with exterior complex scaling, obviates the need for slowly convergent single-center expansions, and allows one to study a variety of electron-molecule collision problems. The method is illustrated by computation of various bound and continuum properties of H + 2 .

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Section: Introductionmentioning

confidence: 99%

Hybrid approach to molecular continuum processes combining Gaussian basis functions and the discrete variable representation

et al. 2005

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“…Our choice of the function g(r) coincides with that in Ref. [24] where the function is characterized by the external radius R 0 and the curvature parameter σ . The representation of the Hamiltonian in the complex coordinates can be found in the same article.…”

Section: Complex Scaling Methodsmentioning

confidence: 97%

“…When properly chosen [24], the curvature parameter σ weakly influences the results, and the value σ = 1.0 was used here. The variation of both the real and imaginary part of the resonances energies with θ was found to be smaller than the reported accuracy within the range 2…”

Section: Resonances For J =mentioning

confidence: 99%

Convergence and quantum number assignment studies of rovibrational eigenstates in a model of predissociating NeICl van der Waals complex

Elander

Levin

Yarevsky

2008

Int J of Quantum Chemistry

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This report details extensions and further analysis of the results presented in an earlier study (Elander et al., Phys Rev A 2001, 64, 012505). Rovibrational resonances in a model of the triatomic van der Waals complex NeICl were studied with a full quantum mechanical, smooth exterior dilation technique realized in a three-dimensional finite element code. Both exact and approximate results, where Coriolis effects are neglected, are presented, and their structures are discussed. Although the helicity is a good quantum number in a one-equation approximation, it is here demonstrated that this is not in the case when including Coriolis coupling, that is, couplings to other helicity components. The behavior of the resonance widths and the positions together with the structure of the resonance wave functions and their dependence on the total angular momentum and its projection have been studied. The dependence of the width of a given resonance on the total angular momentum was found to be weak while the dependence on the helicity is stronger.

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“…The difference between the values calculated for two subsequent polynomial degrees can be used as a crude estimation of the accuracy. Furthermore, more accurate estimations can be constructed based on the known error behavior in the FEM [23]. In the vicinity of the ionization threshold the cross section approaches zero.…”

Section: Electron-hydrogen Scatteringmentioning

confidence: 99%

Potential-splitting approach applied to the Temkin–Poet model for electron scattering off the hydrogen atom and the helium ion

Yarevsky

Yakovlev

Larson

et al. 2015

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

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The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three-body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrödinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.

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Exterior complex scaling method applied to doubly excited states of helium

Cited by 47 publications

References 17 publications

Hybrid approach to molecular continuum processes combining Gaussian basis functions and the discrete variable representation

Hybrid approach to molecular continuum processes combining Gaussian basis functions and the discrete variable representation

Convergence and quantum number assignment studies of rovibrational eigenstates in a model of predissociating NeICl van der Waals complex

Potential-splitting approach applied to the Temkin–Poet model for electron scattering off the hydrogen atom and the helium ion

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