Asymptotic solution of the Schrödinger equation for three charged particles

Alt, E. O.; Mukhamedzhanov, A. M.

doi:10.1103/physreva.47.2004

Cited by 155 publications

(91 citation statements)

References 5 publications

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“…These are the asymptotic conditions in the i regions (with i = 2,3), named after the work of Alt and Mukhamedzhanov [30]. Here η 2,n is the Sommerfeld parameter η 2,n = Z/k n .…”

Section: Fast Electron Regime Modelmentioning

confidence: 99%

“…Here η 2,n is the Sommerfeld parameter η 2,n = Z/k n . The sum in (12) When both electrons are in the continuum, the corresponding asymptotic region is named 0 , and all three particles are far from each other [30]. In such case no contributions coming from bound states are expected in the asymptotic three-body scattering wave function since all interparticle distances are large.…”

Section: Fast Electron Regime Modelmentioning

confidence: 99%

“…The coordinatedependent momentak j (j = 2,3) were defined originally by Alt and Mukhamedzhanov [30], while κ = k When the collision process is studied and the Schrödinger equation is solved numerically, all the channels, represented by the asymptotic wave functions To analyze the ability of the generalized Sturmian methodology to generate a solution containing all the channels, we consider the simpler case of an S-wave model [25]:…”

Section: Fast Electron Regime Modelmentioning

confidence: 99%

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Insights from the zero-angular-momentum wave in single and double ionization of He by fast electrons

2014

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In a recent contribution our group proposed a perturbative approach to deal with the open problem of double ionization of helium by electron impact. The goal of this work is to delve into the physics of the scattering function, and provide evidence of the nature of the single-ionization channels present in the three-body wave function. We show that the fast oscillating parts of the wave function are indeed the single-ionization channels, which appear coupled with the double continuum ones. We found a particular type of basis set within the Generalized Sturmian method that is better suited to isolate single from double-ionization channels.

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“…These are the asymptotic conditions in the i regions (with i = 2,3), named after the work of Alt and Mukhamedzhanov [30]. Here η 2,n is the Sommerfeld parameter η 2,n = Z/k n .…”

Section: Fast Electron Regime Modelmentioning

confidence: 99%

Section: Fast Electron Regime Modelmentioning

confidence: 99%

Section: Fast Electron Regime Modelmentioning

confidence: 99%

See 1 more Smart Citation

Insights from the zero-angular-momentum wave in single and double ionization of He by fast electrons

2014

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“…Let us introduce the asymptotic region Ω α corresponding to the case when two particles β and γ are close to each other while the third particle α is far away. In this region r α /ρ α → 0 at ρ α → ∞ [17]. Also, we denote by Ω 0 the asymptotic region where all three particles are far away (breakup channel), that is r α , ρ α → ∞ and r α /ρ α → const = 0.…”

Section: Three-body Theory Of Deuteron Stripping Populating Boundmentioning

confidence: 99%

Surface-integral formalism of deuteron stripping

et al. 2014

Self Cite

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The purpose of this paper is to develop an alternative theory of deuteron stripping to resonance states based on the surface integral formalism of Kadyrov et al. [Ann. Phys. 324, 1516] and continuum-discretized coupled channels (CDCC). First we demonstrate how the surface integral formalism works in the three-body model and then we consider a more realistic problem in which a composite structure of target nuclei is taken via optical potentials. We explore different choices of channel wave functions and transition operators and show that a conventional CDCC volume matrix element can be written in terms of a surface-integral matrix element, which is peripheral, and an auxiliary matrix element, which determines the contribution of the nuclear interior over the variable r nA . This auxiliary matrix element appears due to the inconsistency in treating of the n − A potential: this potential should be real in the final state to support bound states or resonance scattering and complex in the initial state to describe n − A scattering. Our main result is formulation of the theory of the stripping to resonance states using the prior form of the surface integral formalism and CDCC method. It is demonstrated that the conventional CDCC volume matrix element coincides with the surface matrix element, which converges for the stripping to the resonance state. Also the surface representation (over the variable r nA ) of the stripping matrix element enhances the peripheral part of the amplitude although the internal contribution doesn't disappear and increases with increase of the deuteron energy. We present calculations corroborating our findings for both stripping to the bound state and the resonance. 25.45.Hi, 2

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“…The wave function ⌿ ͑f͒− which belongs to the continuum part ⌿ c − is the unscattered part of the asymptotic wave function ⌿ f − . The general form of the unscattered asymptotic wave function ⌿ ͑f͒− has been derived in [36,37]. This form takes into account the three-body correlation effects.…”

Section: ͑46͒mentioning

confidence: 99%

Theory of Electron Impact Ionization of Atoms

Stelbovics¹,

Bartlett²,

Bray³

et al. 2006

AIP Conference Proceedings

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The existing formulations of electron-impact ionization of a hydrogenic target suffer from a number of formal problems including an ambiguous and phase-divergent definition of the ionization amplitude. An alternative formulation of the theory is given. An integral representation for the ionization amplitude which is free of ambiguity and divergence problems is derived and is shown to have four alternative, but equivalent, forms well suited for practical calculations. The extension to amplitudes of all possible scattering processes taking place in an arbitrary three-body system follows. A well-defined conventional post form of the breakup amplitude valid for arbitrary potentials including the long-range Coulomb interaction is given. Practical approaches are based on partial-wave expansions, so the formulation is also recast in terms of partial waves and partialwave expansions of the asymptotic wave functions are presented. In particular, expansions of the asymptotic forms of the total scattering wave function, developed from both the initial and the final state, for electronimpact ionization of hydrogen are given. Finally, the utility of the present formulation is demonstrated on some well-known model problems.

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Asymptotic solution of the Schrödinger equation for three charged particles

Cited by 155 publications

References 5 publications

Insights from the zero-angular-momentum wave in single and double ionization of He by fast electrons

Insights from the zero-angular-momentum wave in single and double ionization of He by fast electrons

Surface-integral formalism of deuteron stripping

Theory of Electron Impact Ionization of Atoms

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