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Journal of Physics B Atomic Molecular and Optical Physics

Induced transitions in a continuous atomic system spectrum with resonance structure

V A Pazdzersky, V I Usachenko, Alexander B Voitkiv

Published Feb 28, 1988• 2 citations
Publisher

Abstract

The electromagnetic (EM) radiation gain for the induced photorecombination of an electron or ion (atom) into the autoionising state of the atom (negative ion) is considered in terms of the rotating-wave approximation, taking account of free-free transitions. Analytical expressions for the radiation gain coefficient have been derived for long and short times of action of the EM radiation. It has been shown that taking account of the induced direct transitions between the continua results in the 'renormalisation' of natural and ionisation widths of the autoionising state and, under certain conditions, essentially changes the character of the radiation gain; in particular, a typical asymmetric Fano-type profile appears.

DOI
10.1088/0953-4075/21/4/011

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Journal of Physics B Atomic Molecular and Optical Physics•Nov 14, 1990•2 citations
The electromagnetic (EM) radiation gain for the induced photorecombination of an electron or ion (atom) into the autoionising state of the atom (negative ion) is considered in terms of the rotating-wave approximation, taking account of free-free transitions. Analytical expressions for the radiation gain coefficient have been derived for long and short times of action of the EM radiation. It has been shown that taking account of the induced direct transitions between the continua results in the 'renormalisation' of natural and ionisation widths of the autoionising state and, under certain conditions, essentially changes the character of the radiation gain; in particular, a typical asymmetric Fano-type profile appears.
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.
Electron-atom ionisation in the presence of a resonant EM field is considered theoretically, taking the hydrogen atom as an example. The radiation field is taken to have a frequency matching the 1s-2p transition frequency. The theoretical treatment is based on the Coulomb-Born wave approximation and on the two-level atom model. The physical picture arising from the resulting field-assisted triple differential cross section (TDC) is that of ionisation events taking place simultaneously from the ground and the excited 2p states, the role of the radiation field being mainly that of pumping target atoms.
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 rotating wave approximation is used to obtain parametric expressions for the resonance cross section for the atomic ground state ionisation by linearly polarised probe radiation in the vicinity of an autoionisation state coupled resonantly to another autoionisation state through circularly polarised laser radiation. Calculations are made for the 2s2p 1 P and 2s3d 1 D states of the helium atom. It is shown that the structure of the photoionisation cross-section spectrum formed for circularly polarised laser radiation differs qualitatively from the structure formed in the case of linear polarisation. The dependence of this structure on the intensity and frequency of laser radiation and the direction of polarisation of the probe radiation is studied.
A theory of two-photon ionisation of atomic systems is developed incorporating into the treatment details of the laser spectrum. A general expression for the time-integrated two-photon ionisation probability is obtained together with general expressions for the induced shifts and widths of the atomic levels. These expressions are valid near resonance, when in the ordinary perturbation treatment the energy denominators vanish. The general expressions are then evaluated for the special case of a Lorentzian laser spectrum, when simple analytic results are obtained. The treatment is not confined to the two-level atom or the rotating-wave approximation.