Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Unified description of radiative and dielectronic recombination, including the coupling between autoionization and radiation continua

V. L. Jacobs, J. Cooper, Stanley L. Haan

Published Aug 1, 1987• 45 citations
Publisher

Abstract

Although dielectronic and radiative recombination are usually treated as distinct noninterfering processes, Alber, Cooper, and Rau [Phys. Rev. A 30, 2845 (1984)] have recently presented a scattering- or S-matrix analysis which provides a unified description of these processes. This description employs a diagonalization of the atom plus radiation field Hamiltonian using a limited basis set consisting of one discrete autoionizing state, a single-electron continuum, and a single-photon continuum. In the present work we extend Mo?ller scattering operator and resolvent operator techniques, which have previously been used to discuss the decay of prepared systems, in order to provide an S-matrix analysis of the electron-ion photorecombination process near an isolated autoionizing resonance. We explicitly allow for degenerate magnetic sublevels of the atomic system and for multiple angular momentum contributions in the partial-wave expansion of the electron-continuum eigenstate. After the introduction of the pole approximation, in which only the \ensuremath{\delta}-function term is retained in the evaluation of the various self-energies that occur in the diagonalization of the Hamiltonian for the combined many-electron radiation-field system, we obtain the total electron-ion photorecombination cross section as the sum of the radiative and dielectronic recombination contributions together with the conventionally ignored interference term.The radiative and dielectronic recombination cross sections reduce to the familiar forms when the continuum-continuum coupling effects are neglected. Alternatively, the combined cross section for the entire electron-ion photorecombination process may be represented by a modified Fano line profile, which is shifted and broadened as a result of the coupling between the autoionization and radiation continua. Recombination processes that involve more than a single state of the initial ion, of the autoionizing resonance, or of the final system can be treated by appropriately augmenting the unperturbed basis set. It is anticipated that the effects of the interference between radiative and dielectronic recombination and of the continuum-continuum coupling will be most important for individual transitions involving low-lying autoionizing levels and will probably be negligible for the total dielectronic recombination rates due to the highly excited levels.

DOI
10.1103/physreva.36.1093

Related papers

Unified treatment of radiative and dielectronic recombination

G. Alber, J. Cooper, A. R. P. Rau

A coupled-channel analysis of electron-positive ion recombination is carried out, with full treatment of the coupling between radiation and autoionization continua. The cross section for this process reduces in the appropriate limits to the expressions for radiative and dielectronic recombination. The coupling to the radiation continuum leads to a modified Fano profile for the autoionizing resonances. The more complete, combined expressions derived here may be of interest for recent experimental studies of recombination and their comparison with theoretical results.

Physical Review A•Nov 1, 1984•47 citations

Projection-operator approach to the unified treatment of radiative and dielectronic recombination

Stanley L. Haan, V. L. Jacobs

A formalism that is based on projection operators is employed to obtain a general recipe for constructing matrix elements of the transition or T operator for electron-ion photorecombination processes in model systems featuring a limited number of discrete states and continua. The projection-operator formalism allows for a natural separation of the total transition operator into a direct, or radiative recombination, contribution and a resonance, or dielectronic recombination contribution. Implementation of the general recipe is discussed, and expressions for matrix elements of needed propagators in the combined Hilbert space of electron and photon continua are derived for model systems in which one makes the pole approximation on the photon continua, but not on the electron continua. The simplifications that occur when the pole approximation is made on all continua are presented. Finally, the recipe is employed to describe photorecombination for two model systems that feature an isolated autoionizing state. One model includes an arbitrary number of possible final-state photon continua, and the second model includes an arbitrary number of possible final-state electron continua. For the former model, it is shown how the various terms entering into the expression for the recombination transition amplitude can be obtained from a perturbation series and interpreted in terms of Feynman-like diagrams.

Physical Review A•Jul 1, 1989•61 citations

Resonance profiles for electron-ion photorecombination at an isolated resonance

Stanley L. Haan

A projection-operator formalism is employed in studying photorecombination at energies close to an autoionizing resonance. A resonance profile is defined, and is presented without approximation for a model system consisting of one electron continuum, one autoionizing state, and one final radiatively stabilized atomic state. Effective line-profile parameters \ensuremath{\varepsilon}^ and q^ are defined, and the photorecombination resonance profile is shown to be the same as the photoionization resonance profile (for the process in which initial and final atomic states are interchanged from the photorecombination process), provided one-photon spontaneous radiative decay effects are included. The effective line-profile parameters are examined, and are shown to reduce to the standard autoionization line-profile parameters in the limit of no spontaneous radiative decay. Effective line-profile parameters are also defined in the pole approximation for two model systems featuring an isolated autoionizing state. Comparison is made with effective line-profile parameters that have been defined elsewhere in the context of photoionization into coupled electron-continuum channels. The similarity in mathematical formalism for systems supporting multiple continua, regardless of whether these continua are electron or photon continua, is discussed.

Physical Review A•Oct 1, 1989•5 citations

Liouville-spaceR-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

V. L. Jacobs, Philip George Burke, R. M. Potvliege

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 8, 2014•1 citation

Effects of radiative decay on the bound-continuum transition of highly charged atomic ions

Kazuhiro Sakimoto, Mariko Terao-Dunseath, KEITH A. BERRINGTON

In a system consisting of an electron and a highly charged ion, interaction with the radiation field is strong, and radiation-damping effects must be accurately taken into account. The present work provides a numerical method to study the radiation-damping effect in the processes of photoionization, radiative recombination, and electron scattering. A simple calculation is made for ${\mathrm{Fe}}^{24+}$, ${\mathrm{Xe}}^{52+}$(1s2s)+h\ensuremath{\nu}\ensuremath{\leftrightarrows}${\mathrm{Fe}}^{25+}$, ${\mathrm{Xe}}^{53+}$(1s)+e. Special emphasis is placed on the nonapplicability of conventional first-order perturbation theory to photoinduced autoionization of a highly charged ion. The interference effect between the resonant and the nonresonant parts is found to be negligible in the present cases.

Physical Review A•Jul 1, 1990•41 citations

Resonant electron scattering and dielectronic recombination in two-center atomic systems

A. Eckey, A. Jacob, Alexander B Voitkiv +1 more

Electron scattering and dielectronic recombination with an ion in the presence of a neighboring atom is studied. The incident electron is assumed to be captured by the ion, leading to resonant excitation of the atom which afterwards may stabilize either by electron reemission or radiative decay. We show that the participation of the atom can strongly affect, both quantitatively and qualitatively, the corresponding processes of electron scattering and recombination. Various ion-atom systems and electronic transitions are considered. In particular we show that electron scattering under backward angles may be strongly enhanced, provided the incident energy lies very close to the resonance. Besides, we derive the scaling behavior of two-center dielectronic recombination with the principal quantum numbers of the participating atomic states. The resonant enhancement in this process is shown to be so strong that it can compete with ordinary single-center recombination even after integrating over a rather broad distribution of incident electron energies.

arXiv:1805.03458•Physical Review A•Jul 23, 2018•12 citations
Although dielectronic and radiative recombination are usually treated as distinct noninterfering processes, Alber, Cooper, and Rau [Phys. Rev. A 30, 2845 (1984)] have recently presented a scattering- or S-matrix analysis which provides a unified description of these processes. This description employs a diagonalization of the atom plus radiation field Hamiltonian using a limited basis set consisting of one discrete autoionizing state, a single-electron continuum, and a single-photon continuum. In the present work we extend Mo?ller scattering operator and resolvent operator techniques, which have previously been used to discuss the decay of prepared systems, in order to provide an S-matrix analysis of the electron-ion photorecombination process near an isolated autoionizing resonance. We explicitly allow for degenerate magnetic sublevels of the atomic system and for multiple angular momentum contributions in the partial-wave expansion of the electron-continuum eigenstate. After the introduction of the pole approximation, in which only the \ensuremath{\delta}-function term is retained in the evaluation of the various self-energies that occur in the diagonalization of the Hamiltonian for the combined many-electron radiation-field system, we obtain the total electron-ion photorecombination cross section as the sum of the radiative and dielectronic recombination contributions together with the conventionally ignored interference term.The radiative and dielectronic recombination cross sections reduce to the familiar forms when the continuum-continuum coupling effects are neglected. Alternatively, the combined cross section for the entire electron-ion photorecombination process may be represented by a modified Fano line profile, which is shifted and broadened as a result of the coupling between the autoionization and radiation continua. Recombination processes that involve more than a single state of the initial ion, of the autoionizing resonance, or of the final system can be treated by appropriately augmenting the unperturbed basis set. It is anticipated that the effects of the interference between radiative and dielectronic recombination and of the continuum-continuum coupling will be most important for individual transitions involving low-lying autoionizing levels and will probably be negligible for the total dielectronic recombination rates due to the highly excited levels.
A coupled-channel analysis of electron-positive ion recombination is carried out, with full treatment of the coupling between radiation and autoionization continua. The cross section for this process reduces in the appropriate limits to the expressions for radiative and dielectronic recombination. The coupling to the radiation continuum leads to a modified Fano profile for the autoionizing resonances. The more complete, combined expressions derived here may be of interest for recent experimental studies of recombination and their comparison with theoretical results.
A formalism that is based on projection operators is employed to obtain a general recipe for constructing matrix elements of the transition or T operator for electron-ion photorecombination processes in model systems featuring a limited number of discrete states and continua. The projection-operator formalism allows for a natural separation of the total transition operator into a direct, or radiative recombination, contribution and a resonance, or dielectronic recombination contribution. Implementation of the general recipe is discussed, and expressions for matrix elements of needed propagators in the combined Hilbert space of electron and photon continua are derived for model systems in which one makes the pole approximation on the photon continua, but not on the electron continua. The simplifications that occur when the pole approximation is made on all continua are presented. Finally, the recipe is employed to describe photorecombination for two model systems that feature an isolated autoionizing state. One model includes an arbitrary number of possible final-state photon continua, and the second model includes an arbitrary number of possible final-state electron continua. For the former model, it is shown how the various terms entering into the expression for the recombination transition amplitude can be obtained from a perturbation series and interpreted in terms of Feynman-like diagrams.
A projection-operator formalism is employed in studying photorecombination at energies close to an autoionizing resonance. A resonance profile is defined, and is presented without approximation for a model system consisting of one electron continuum, one autoionizing state, and one final radiatively stabilized atomic state. Effective line-profile parameters \ensuremath{\varepsilon}^ and q^ are defined, and the photorecombination resonance profile is shown to be the same as the photoionization resonance profile (for the process in which initial and final atomic states are interchanged from the photorecombination process), provided one-photon spontaneous radiative decay effects are included. The effective line-profile parameters are examined, and are shown to reduce to the standard autoionization line-profile parameters in the limit of no spontaneous radiative decay. Effective line-profile parameters are also defined in the pole approximation for two model systems featuring an isolated autoionizing state. Comparison is made with effective line-profile parameters that have been defined elsewhere in the context of photoionization into coupled electron-continuum channels. The similarity in mathematical formalism for systems supporting multiple continua, regardless of whether these continua are electron or photon continua, is discussed.
A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.
In a system consisting of an electron and a highly charged ion, interaction with the radiation field is strong, and radiation-damping effects must be accurately taken into account. The present work provides a numerical method to study the radiation-damping effect in the processes of photoionization, radiative recombination, and electron scattering. A simple calculation is made for Fe24+{\mathrm{Fe}}^{24+}Fe24+, Xe52+{\mathrm{Xe}}^{52+}Xe52+(1s2s)+h\ensuremath{\nu}\ensuremath{\leftrightarrows}Fe25+{\mathrm{Fe}}^{25+}Fe25+, Xe53+{\mathrm{Xe}}^{53+}Xe53+(1s)+e. Special emphasis is placed on the nonapplicability of conventional first-order perturbation theory to photoinduced autoionization of a highly charged ion. The interference effect between the resonant and the nonresonant parts is found to be negligible in the present cases.
Electron scattering and dielectronic recombination with an ion in the presence of a neighboring atom is studied. The incident electron is assumed to be captured by the ion, leading to resonant excitation of the atom which afterwards may stabilize either by electron reemission or radiative decay. We show that the participation of the atom can strongly affect, both quantitatively and qualitatively, the corresponding processes of electron scattering and recombination. Various ion-atom systems and electronic transitions are considered. In particular we show that electron scattering under backward angles may be strongly enhanced, provided the incident energy lies very close to the resonance. Besides, we derive the scaling behavior of two-center dielectronic recombination with the principal quantum numbers of the participating atomic states. The resonant enhancement in this process is shown to be so strong that it can compete with ordinary single-center recombination even after integrating over a rather broad distribution of incident electron energies.