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Physical Review A

Control of autoionization widths: Doubly excited coherent elliptic states

Daniel Janby, Lars Bojer Madsen, Valentin N. Ostrovsky

Published Jun 8, 2006• 3 citations
Publisher

Abstract

Doubly excited coherent elliptic states (DECESs) of an atom could be produced by exciting an atomic electron to a Rydberg state, applying the adiabatic field-switching technique to obtain a coherent elliptic state (CES) and by subsequent excitation of an atomic core electron into a low-lying excited state. The DECESs decay by autoionization and radiative transitions. As an example, the autoionization widths are calculated for DECESs in He. The dependence of the widths on the eccentricity of the CES, principal quantum number of the Rydberg electron, orientation of the inner electron orbital and electron exchange is studied and interpreted.

DOI
10.1103/physreva.73.062708

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Doubly excited coherent elliptic states (DECESs) of an atom could be produced by exciting an atomic electron to a Rydberg state, applying the adiabatic field-switching technique to obtain a coherent elliptic state (CES) and by subsequent excitation of an atomic core electron into a low-lying excited state. The DECESs decay by autoionization and radiative transitions. As an example, the autoionization widths are calculated for DECESs in He. The dependence of the widths on the eccentricity of the CES, principal quantum number of the Rydberg electron, orientation of the inner electron orbital and electron exchange is studied and interpreted.
Electron capture cross sections for coherent elliptic Rydberg states have been measured as a function of eccentricity. The ion impact velocity was parallel to the minor axis of the associated, classical elliptic orbit and both clockwise and anticlockwise orbital motion of the electron were studied. The incoming ions were 2.5 keV 23 Na + and the Rydberg target, with principal quantum number n=25, was formed by laser excitation of Li atoms with subsequent adiabatic switching of crossed, external electric and magnetic fields. A strong dependence on eccentricity and sense of orbital motion was found.
Oriented elliptic Rydberg atoms have been formed in a thermal beam of Li atoms by the adiabatic crossed-field method. All coherent elliptic quantum states from linear to circular can be produced by this method. The orientation and eccentricity is controlled by the external fields. While the formation of circular states by the crossed-field method has already been established experimentally, the radiative decay of the Rydberg atoms formed here was measured and compared with theory to verify that highly eccentric elliptic quantum states may also be formed.
The linear-Stark-effect approximation is employed to investigate the effects of electric fields on autoionizing doubly excited atomic states corresponding to relatively large values of the outer-electron principal quantum number nnn. By assuming that a statistical distribution of the inner-electron magnetic sublevels has been established, simple expressions are derived which relate the autoionization and radiative transition rates in the presence of an electric field to the respective field-free rates. It is pointed out that the multiphoton laser excitation of the doubly excited states can give rise to a nonstatistical distribution of the magnetic sublevels and to complex interference terms involving transition amplitudes associated with different values of the outer-electron angular momentum quantum number lll. The results of calculations are presented for the autoionization and radiative-transition rates which play the most important role in the dielectronic recombination of the Li-like Fe+23{\mathrm{Fe}}^{+23}Fe+23 ion through the $2p\ensuremath{\rightarrow}2s$ inner-electron transition, where the contributions from large-nnn values are particularly important. In these calculations it is assumed that the magnetic sublevels are statistically populated and only the simple expressions for the transition rates are employed. The effects of the electric field on the dominant (inner-electron) radiative decay rate can be neglected, but the electric field mixing of the outer-electron lll substates substantially increases the autoionization rates from the higher-lll sublevels.
This paper is devoted to the autoionization process of large-angular-momentum Rydberg states. After a brief account of autoionization formalism in nonrelativistic theory and single-configuration approximation, we apply it to atomic states with one electron of large angular momentum. The dominant contribution is the direct one and the exchange contribution is ignored. In this framework, the autoionization width varies with the principal quantum number as ${n}^{\mathrm{\ensuremath{-}}3}$ and exponentially with the angular momentum. When two excited electrons interact with a spherically symmetric core, it is demonstrated that the interaction between the Rydberg electron and the core polarized by the valence electron is proportional to the interaction between the two active electrons. Using newly derived radial matrix elements, we obtain a generally good agreement between our results and experiments on barium and strontium. Large-l Rydberg states are shown to be stable versus autoionization as soon as l is about 7. Possible refinements of our method are reviewed.
This paper presents the coherent elliptic states (CES) of alkaline constructed from the spherical Rydberg wavefunctions generated by the B-spline method associated with Hartree–Fock approximation. To construct the elliptic orbit for alkaline is not straightforward. The core effect plays an important role for the formation of elliptic states especially in higher and lower eccentricity. When the eccentricity is not large (i.e. e=0.6), the physical quantities of CES of alkaline atoms can be theoretically calculated by the replacement with hydrogen atom.