Approach to electron-impact ionization that avoids the three-body Coulomb asymptotic form

McCurdy, C. William; Rescigno, T. N.; Byrum, D.

doi:10.1103/physreva.56.1958

Cited by 68 publications

(42 citation statements)

References 36 publications

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“…However, it was not until 1997 that Rescigno et al [44] began exploring the use of ECS for three-body ionizing collisions, which culminated in their landmark publication in Science [22] of the first complete solution to an e-H break-up problem. These publications, along with [24,45], should be referenced for a detailed description and theoretical justification of the ECS transformation; here we will use a simple one-dimensional example to give some insight into the workings of ECS.…”

Section: Exterior Complex Scalingmentioning

confidence: 99%

A complete numerical approach to electron–hydrogen collisions

Bartlett

2006

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

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This tutorial presents an extensive computational study of electron-impact scattering and ionization of atomic hydrogen and hydrogenic ions, through the solution of the non-relativistic Schrödinger equation in coordinate space using propagating exterior complex scaling (PECS). It details the complete numerical and computational development of the PECS method, which enables highly computationally-efficient solution of these collision systems. Benchmark results are presented for a complete range of electron-hydrogen collisions, including discrete elastic and inelastic scattering both below and above the ionization threshold energy, very low-energy ionizing collisions through to moderately high-energy ionizing collisions, ground-state and excited-state targets and charged hydrogenic targets with Z 4. Total ionization cross sections through to fully differential cross sections, both in-plane and out-ofplane, are given and are found to be in excellent accord with other state-of-theart methods and measurements, where available. We also review our recent confirmation (Bartlett and Stelbovics 2004 Phys. Rev. Lett. 93 233201) of the Wannier and related threshold laws for e-H collisions.

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Section: Exterior Complex Scalingmentioning

confidence: 99%

A complete numerical approach to electron–hydrogen collisions

Bartlett

2006

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

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“…Here the subscript a denotes either the total, ionization or excitation cross section, and P a represents the corresponding projection operator [5].…”

Section: Calculation Of Amplitudes and Cross Sectionsmentioning

confidence: 99%

“…[5,20,25,27] and references therein). In this report, however, we focus mainly on the calculation of the wave function, and we consider the differential ionization cross section outside the scope of the paper.…”

Section: Calculation Of Amplitudes and Cross Sectionsmentioning

confidence: 99%

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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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“…We avoid having to explicitly specify the asymptotic form for ionization by calculating the ψ L l 1 l 2 on a complex contour [20,16]. This transformation of the Schrödinger equation, called exterior complex scaling (ECS), was invented by Simon [24] to study molecular resonances in scattering theory.…”

Section: Simplifying the Boundary Conditionsmentioning

confidence: 99%

Solution of a three-body problem in quantum mechanics using sparse linear algebra on parallel computers

Baertschy

2001

Proceedings of the 2001 ACM/IEEE Conference on Supercomputing

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A complete description of two outgoing electrons following an ionizing collision between a single electron and an atom or molecule has long stood as one of the unsolved fundamental problems in quantum collision theory. In this paper we describe our use of distributed memory parallel computers to calculate a fully converged wave function describing the electron-impact ionization of hydrogen. Our approach hinges on a transformation of the Schrödinger equation that simplifies the boundary conditions but requires solving very ill-conditioned systems of a few million complex, sparse linear equations. We developed a two-level iterative algorithm that requires repeated solution of sets of a few hundred thousand linear equations. These are solved directly by LUfactorization using a specially tuned, distributed memory parallel version of the sparse LU -factorization library SuperLU. In smaller cases, where direct solution is technically possible, our iterative algorithm still gives significant savings in time and memory despite lower megaflop rates.

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Approach to electron-impact ionization that avoids the three-body Coulomb asymptotic form

Cited by 68 publications

References 36 publications

A complete numerical approach to electron–hydrogen collisions

A complete numerical approach to electron–hydrogen collisions

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

Solution of a three-body problem in quantum mechanics using sparse linear algebra on parallel computers

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