Making complex scaling work for long-range potentials

Rescigno, T. N.; Baertschy, Mark; Byrum, D.; McCurdy, C. W.

doi:10.1103/physreva.55.4253

Cited by 113 publications

(133 citation statements)

References 32 publications

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“…Equation (46) reduces to (43) for fixed grid spacing (α = 1), and (47) reduces to zero. In this case the error is given by the next term in the series, which for α = 1 reduces to (44). This one-dimensional formula is readily extended to two dimensions using similar techniques to Poet [30].…”

Section: Numerov Formulaementioning

confidence: 99%

“…Many decades prior to this the complex rotation of the radial coordinates had been used for atomic resonance problems. 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%

“…Though the ECS technique has been demonstrated with both finite element and finite-difference numerical methods [22,44], we will restrict our discussion to numerical grids that support finite-difference methods suitable for use with the propagation technique introduced later.…”

Section: Numerical Gridmentioning

confidence: 99%

“…A discontinuity in the first derivative of the transformed wavefunction is observed at R 0 , which affects the grid spacing required in this region. Rescigno et al [44] showed that the ECS transformation is valid for use with finite-difference methods, provided that the point of rotation into the complex plane R 0 is one of the points on the numerical grid.…”

Section: Exterior Complex Scalingmentioning

confidence: 99%

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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: Numerov Formulaementioning

confidence: 99%

Section: Exterior Complex Scalingmentioning

confidence: 99%

Section: Numerical Gridmentioning

confidence: 99%

Section: Exterior Complex Scalingmentioning

confidence: 99%

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A complete numerical approach to electron–hydrogen collisions

Bartlett

2006

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

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“…We use the FE functions from Refs. [57,58]. On the interval [0,1] we construct six unique, linearly independent fifth-order Hermite interpolating polynomials satisfying the boundary conditions…”

Section: Finite-element Methodsmentioning

confidence: 99%

Stability of the time-dependent configuration-interaction-singles method in the attosecond and strong-field regimes: A study of basis sets and absorption methods

et al. 2016

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We investigate the behavior of several spatial grid methods and complex absorbers for strong-field and attosecond scenarios when using the time-dependent configuration-interaction singles method to solve the multielectron time-dependent Schrödinger equation for atoms. We compare the pseudospectral grid, finite-element, and finite-element-discrete-variable-representation (DVR) methods with each other and discuss their advantages and disadvantages. Additionally, we study the performances of complex absorbing potential (CAP) and smooth exterior complex scaling (SES) to absorb the outgoing electron. We find that SES performs generally better than CAP for calculating high-harmonic generation spectra and XUV photoelectron spectra. In both of these cases, the DVR and even more the FEM grid representations show more reliable results-especially when using SES. Both absorbers show drawbacks when calculating photoelectron spectra in the strong-field regime.

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Recent Advances in the Study of Negative‐Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential

Das

Samanta

2022

ChemPhysChem

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The transient resonances are a challenge to bound state quantum mechanics. These states lie in the continuum part of the spectrum of the Hamiltonian. For this, one has to treat a continuum problem due to electron‐molecule scattering and the many‐electron correlation problem simultaneously. Moreover, the description of a resonance requires a wavefunction that bridges the part that resembles a bound state with another that resembles a continuum state such that the continuity of the wavefunction and its first derivative with respect to the distance between the incoming projectile and the target is maintained. A review of the recent advances in the theoretical investigation of the negative‐ion resonances (NIR) is presented. The NIRs are ubiquitous in nature. They result from the scattering of electrons off of an atomic or molecular target. They are important for numerous chemical processes in upper atmosphere, space and even biological systems. A contextual background of the existing theoretical methods as well as the newly‐developed multiconfigurational propagator tools based on a complex absorbing potential are discussed.

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Making complex scaling work for long-range potentials

Cited by 113 publications

References 32 publications

A complete numerical approach to electron–hydrogen collisions

A complete numerical approach to electron–hydrogen collisions

Stability of the time-dependent configuration-interaction-singles method in the attosecond and strong-field regimes: A study of basis sets and absorption methods

Recent Advances in the Study of Negative‐Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential

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