<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-wave model for H-like ions

Bray, Igor; Clare, Bradley A.

doi:10.1103/physreva.56.r1694

Cited by 13 publications

(9 citation statements)

References 25 publications

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“…The generalization of that technique seems to be relatively straightforward but remains to be done in detail. Comparing the results in papers [16][17][18][19] to our results we find that our approach demonstrates both good stability and a high accuracy for the scattering problem. In contrast to the close-coupling and R-matrix approaches [17], our calculations do not suffer from artificial noise and oscillations.…”

Section: Electron-he + Scatteringsupporting

confidence: 63%

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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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Section: Electron-he + Scatteringsupporting

confidence: 63%

“…There exist a few studies of electron-He + scattering in the literature. We would like to mention results calculated with the the convergent close-coupling method [16][17][18], the R-matrix method [16,17,19] which all are applied to the TP model. Using Eq.…”

Section: Electron-he + 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 N hydrogen (H) states were obtained by diagonalising the Hamiltonian with λ ≈ 1.0. The minor variation in λ was made to ensure that the total energy E was exactly half-way between two adjacent pseudothresholds, as the underlying integration rule requires [32,33]. The positronium (Ps) states were obtained by diagonalising the corresponding Hamiltonian with λ ′ = 0.5.…”

mentioning

confidence: 99%

“…The N hydrogen states were obtained by diagonalizing the hydrogen Hamiltonian with λ ≈ 2.0, and the N positronium states obtained with λ ≈ 1.0. Minor variation from the given values was made to ensure that the total energy was exactly half way between two adjacent pseudothresholds, as the underlying integration rule requires Stelbovics 1995, Bray andClare 1997).…”

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confidence: 99%

Convergence of two-centre expansions in positron-hydrogen collisions

Kadyrov

Bray

2000

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

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The positron-hydrogen atom scattering system is considered within the S-wave model. Convergence in the elastic scattering, excitation, ionization, and positronium formation channels is studied as a function of the number and type of states used to expand the total wave function. It is found that all unphysical resonances disappear only if near-complete pseudostate expansions are applied to both the atomic and positronium centers. 34.85.+xIn recent years there has been substantial progress in the field of electron-atom collisions. Close-coupling based methods, utilizing near-complete pseudostate expansions about the atomic center, have been shown to yield very accurate results for discrete excitation and ionization channels, see for example [1][2][3][4]. This progress is primarily based on the study of the electron-hydrogen atom scattering S-wave model (only states with zero orbital angular momentum are retained) performed by Bray and Stelbovics [5]. They showed, by simply taking a pseudostate expansion whose completeness improves with increasing number of states N , that cross sections for discrete and ionization channels converged at all energies. Pseudoresonances, typically associated with small N calculations, disappeared for sufficiently large N , and convergence was to the correct independently evaluated results. This was an extraordinarily powerful result that is at the base of the substantial success recently enjoyed by the various implementations of the close-coupling theories.The situation for positron-atom scattering is somewhat more complicated. In addition to the atomically centered states the positronium formation channel needs to be included in the calculations in order to allow for all possible scattering channels. In other words, one needs a combined basis consisting of two independent basis sets. However, in this case if each of the components of the basis is large enough, one may expect instabilities in the calculations. The reason for this is that at small distances between colliding fragments functions of different basis components may essentially repeat each other due to their nonorthogonality. Thus, the closecoupling problem with the combined-basis-expansions * electronic address: Alisher.Kadyrov@flinders.edu.au is ill-conditioned. Is this an insurmountable obstacle? This question has remained unanswered for a long time. Mitroy, Berge, and Stelbovics [6] and Mitroy and Ratnavelu [7] have performed convergence studies for the full positron-hydrogen problem at low energies. Below the first hydrogen excitation threshold they showed good agreement between large pseudostate close coupling calculations and the highly accurate variational calculations of Humberston [8]. However, at higher energies, particularly above the ionization threshold the situation is less clear.We adopt the often-used CC(N, N ′ ) notation for closecoupling calculations that utilise N atomic eigenstates and N ′ positronium eigenstates to expand the total scattering wave function. In addition, a bar, when applied to N or N ′ ...

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“…The total energy E = 54.4 − 13.6 eV is such that there is a "closed" state for each l (two for S-states). Bray and Clare (1997) discussed, by reference to the equivalent quadrature idea, the importance of having the total energy bisect two of the pseudothresholds. This is particularly important for small N 0 and E. Unfortunately we are unable to have both an energy level at 5 eV and ensure that E is inbetween two other energy levels.…”

Section: Incident Electron Energy 544 Evmentioning

confidence: 99%

Electron-impact ionisation of atomic hydrogen from near threshold to high energies

Bray

2000

Aust. J. Phys.

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Application of the convergent close-coupling (CCC) method to electronimpact ionization of the ground state of atomic hydrogen is considered at incident energies of 15.6, 17.6, 20, 25, 27.2, 30, 54.4, 150 and 250 eV. Total through to fully differential cross sections are presented. Following the analysis of Stelbovics [submitted to Phys. Rev. Lett. (http://xxx.lanl.gov/abs/physics/9905020)] the equal-energy sharing cross sections are calculated using a solely coherent combination of total-spindependent ionization amplitudes, which are found to be simply a factor of two greater than the incoherent combination suggested by Fursa [1996 Phys. Rev. A 54, 2991]. As a consequence, the CCC theory is particularly suited to the equalenergy-sharing kinematical region, and is able to obtain convergent absolute scattering amplitudes, fully ab initio. This is consistent with the step-function hypothesis of Bray [1997 Phys. Rev. Lett. 78, 4721], and indicates that at equal-energy-sharing the CCC amplitudes converge to half the step size. Comparison with experiment is satisfactory in some cases and substantial discrepancies are identified in others. The discrepancies are generally unpredictable and some internal inconsistencies in the experimental data are identified. Accordingly, new (e,2e) measurements are requested.

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S-wave model for H-like ions

Cited by 13 publications

References 25 publications

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

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

Convergence of two-centre expansions in positron-hydrogen collisions

Electron-impact ionisation of atomic hydrogen from near threshold to high energies

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