General time-independent theory of ionization and breakup reactions

Rosenberg, Leonard

doi:10.1088/0953-4075/41/15/155203

Cited by 5 publications

(16 citation statements)

References 19 publications

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“…The same result for the Coulomb S-matrix has also been obtained by different methods by Barut and Rasmussen [30], Fronsdal and Lundberg [31] and Herbst [32]. Important contributions were made to this subject also by Kulish and Fadeev [33], Rosenberg [34][35][36] and Bajzer [37], and it has been reviewed by Chandler [38,39]. A complete time-dependent, many-particle collision theory, which incorporates both exchange and long-range potentials (including the Coulomb potential), has been given by Bencze and Chandler [40].…”

Section: Introductionsupporting

confidence: 68%

“…We will follow here the treatment of Kulish and Fadeev [33], Veselova [29], Rosenberg [34][35][36] and Chandler and Gibson [28] in an attempt to modify the treatment of Csanak et al [1,2] so that it is applicable for ionic targets. The latter treatment, which was relevant for atoms, was in turn based on the wave-packet treatment of scattering by Rodberg and Thaler [49].…”

Section: Incident Electron As a Distinguishable Particlementioning

confidence: 99%

“…It was shown by Veselova [29] and Bajzer [37] for Coulombic potentials (i.e. potentials whose asymptotic form is like that of the Coulomb potential), and subsequently by Rosenberg [34,36] for the electron-ion scattering problem, that the S-matrix elements under those conditions can be written in the factorized form…”

Section: The Formulation Of the Multipole Cross Sections For Electron...mentioning

confidence: 99%

“…In this work, we will follow the wave-packet propagation approach of Csanak et al [1,2], properly modified according to Dollard [25], Kulish and Fadeev [33], Chandler and Gibson [28], Rosenberg [34][35][36] and Bencze and Chandler [40] to take into account the long-range Coulomb potential as well as exchange effects. We will define the multipole creation, destruction and transfer cross sections for electron scattering by ions and we will show how the Dollard definition of the electron-ion scattering operator can be related to some calculational schemes that have been used in the past for electron-ion scattering.…”

Section: Introductionmentioning

confidence: 99%

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The creation, destruction and transfer of multipole moments in electron scattering by ions

Csanak

Fontes

Inal

et al. 2012

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

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Expanding on previous works that involved the scattering of electrons by atoms, we use the wave-packet propagation scheme of Dollard to define multipole moment creation, destruction and transfer cross sections for elastic and inelastic scattering of electrons by ions. We find that our cross section formulae for inelastic scattering agree with those obtained by Fujimoto and coworkers, who used semi-classical collision theory and the impact approximation, but differ from the expressions obtained by them for elastic scattering cross sections. This latter result is due to the fact that Dollard’s theory takes into account the concept that, in the case of electron–ion scattering, the incident and scattered electrons are asymptotically not free. In addition, we apply the Gell-Mann–Goldberger (‘two-potential’) formula in order to provide an unambiguous definition of elastic cross sections, as well as to provide a convenient way of obtaining practical expressions associated with well-established methods, such as the Coulomb–Born and distorted-wave approximations. The present theoretical framework will be the basis for numerical calculations considering specific examples in a future work.

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Section: Introductionsupporting

confidence: 68%

Section: Incident Electron As a Distinguishable Particlementioning

confidence: 99%

Section: The Formulation Of the Multipole Cross Sections For Electron...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The creation, destruction and transfer of multipole moments in electron scattering by ions

Csanak

Fontes

Inal

et al. 2012

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

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“…The method has been extended to breakup in a system of three charged particles in [30]. Extension to a system of arbitrary number of charged particles is given in [74].…”

Section: Introductionmentioning

confidence: 99%

Surface-integral formulation of scattering theory

et al. 2009

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a b s t r a c tWe formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surfaceintegrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.

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Relativistic theory of electron-impact ionization

Rosenberg¹

2010

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

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A relativistic version of an earlier, non-relativistic, formulation of the theory of ionization of an atomic system by electron impact is presented. With a time-independent resolvent operator taken as the basis for the dynamics, a wave equation is derived for a system with open channels consisting of two positive-energy electrons in an external field generated by the residual ion. Virtual intermediate states can be accounted for by the effective Hamiltonian that appears in the wave equation and which in principle may be constructed perturbatively. The asymptotic form of the wavefunction, modified by the effects of the long-range Coulomb interactions of the two electrons in the external field, is derived. These electrons are constrained, by projection operators which appear naturally in the theory, to propagate in positive-energy states only. The long-range Coulomb effects take the form of phase factors similar to those that are found in the non-relativistic version of the theory. With the boundary conditions established, an integral identity for the ionization amplitude is derived, and used to set up a distorted-wave Born expansion for the transition amplitude involving Coulomb-modified propagating waves.

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General time-independent theory of ionization and breakup reactions

Cited by 5 publications

References 19 publications

The creation, destruction and transfer of multipole moments in electron scattering by ions

The creation, destruction and transfer of multipole moments in electron scattering by ions

Surface-integral formulation of scattering theory

Relativistic theory of electron-impact ionization

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