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Physical Review A

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

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

Published Jul 1, 1990• 41 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.42.291

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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.
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.
The effect of a low-frequency laser field on photoionization and radiative recombination processes is studied theoretically, with particular attention paid to the combined influence of the electron-ion Coulomb interaction and the laser field on continuum states of the system. A procedure for representing the asymptotic states of the system, with both long-range interactions properly accounted for, is described. The transition rates are strongly affected by the existence of a Rydberg series of resonances. Methods developed for describing similar resonant processs that occur in the field-free case are generalized here to include the effects of the external laser field. A simple model, based on parametrizations of the type employed in quantum-defect theory, is used to study the modification of resonant structures in the cross section introduced by the external field. In the weak-field limit, a low-frequency approximation for bound-state Compton scattering is obtained, with resonance effects accounted for.
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part,we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluorescence spectrum. Furthermore, we investigate the level structure of heavy hydrogenlike ions in laser beams. Interaction with the light field leads to dynamic shifts of the electronic energy levels, which is relevant for spectroscopic experiments. We apply a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the dipole approximation and takes into account non-dipole effects of retardation and interaction with the magnetic field components of the laser beam. We predicted cross sections for the inter-shell trielectronic recombination (TR) and quadruelectronic recombination processes which have been experimentally confirmed in electron beam ion trap measurements, mainly for C-like ions, of Ar, Fe and Kr. For Kr30+, inter-shell TR contributions of nearly 6% to the total resonant photorecombination rate were found.
A theory describing the radiative decay of an autoionizing state under strong pumping by a coherent field is developed. The theory systematically takes into account the radiative decay of the unperturbed continuum. The problem at hand corresponds to the case of strongly coupled bound states decaying to electron and photon continua with the two continua also weakly coupled to each other. A master equation describing the time evolution of the atomic system is derived, and its exact solution under arbitrary initial conditions is given. The effect of radiative decay on the Fano profiles and photoelectron spectra is analyzed in detail. The time development of the system is also examined. The radiative decay of the autoionizing state and the unperturbed continuum changes the spectra in a significant way. The characteristics of the spectra are correlated with the dressed states (with complex energies) of the system. The changes in the structure of the dressed states as a function of the system parameters such as the spontaneous-emission rate and laser intensity are discussed in detail.
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.
Absorption properties of a system consisting of two autoionizing states coupled strongly either by internal interactions or by external fields are investigated. The autoionizing states may themselves correspond to those induced by laser fields as in resonant multiphoton ionization. The analysis is based on the density matrices and incoherent processes like spontaneous emission and radiative recombination are included. Optical susceptibilities exist in a number of special cases for autoionizing transitions. Exact results for such optical susceptibilities are obtained. Explicit numerical results for susceptibilities, corresponding traditionally to strong-field inverse Raman effect, are given with a view to recent work on dc-field-coupled autoionizing states and on laser-induced autoionization. The behavior of both absorptive and dispersive parts is discussed for a range of parameters.