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Physical Review A

Unified treatment of radiative and dielectronic recombination

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

Published Nov 1, 1984• 47 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.30.2845

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

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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.

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Enhancement of dielectronic recombination in combined electric and magnetic fields

E. S. Shuman, Wensha Yang, Thomas F. Gallagher

We report the enhancement of dielectronic recombination from a continuum of finite bandwidth in combined electric and magnetic fields. Specifically, we have examined the process Ba $6{p}_{3/2}8g\ensuremath{\rightarrow}6{p}_{1/2}ng\ensuremath{\rightarrow}6{s}_{1/2}ng+h\ensuremath{\nu}$ for $32\ensuremath{\le}n\ensuremath{\le}47$ in combined fields ranging from 0 to 7 V/cm and 0 to 250 G. The results demonstrate that it is the component of $B\ensuremath{\perp}E$ that leads to enhancement. The experimental results indicate that the $\mathit{B}$ field coupling must exceed the radiative rate, the autoionization rate, and the Stark splitting of the intermediate autoionizing Rydberg states.

Physical Review A•Jun 23, 2008•0 citations
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.
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 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 small electric field is shown to increase the dielectronic recombination, via autoionizing Rydberg states, of an electron from a continuum of finite bandwidth. The continuum of finite bandwidth is a broad autoionizing state which is part of a series converging to a higher limit, and the field enhancement of the rate occurs because the field converts the nl Rydberg states to nk Stark states, increasing the number of contributing recombination paths. The experimental results are in excellent agreement with the predictions of an isolated resonance approximation treatment and show clearly both the positive effect of Stark mixing and the negative effect of field ionization on dielectronic recombination.
We report the enhancement of dielectronic recombination from a continuum of finite bandwidth in combined electric and magnetic fields. Specifically, we have examined the process Ba $6{p}_{3/2}8g\ensuremath{\rightarrow}6{p}_{1/2}ng\ensuremath{\rightarrow}6{s}_{1/2}ng+h\ensuremath{\nu}$ for $32\ensuremath{\le}n\ensuremath{\le}47$ in combined fields ranging from 0 to 7 V/cm and 0 to 250 G. The results demonstrate that it is the component of $B\ensuremath{\perp}E$ that leads to enhancement. The experimental results indicate that the B\mathit{B}B field coupling must exceed the radiative rate, the autoionization rate, and the Stark splitting of the intermediate autoionizing Rydberg states.