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Physical Review A

Properties of Rydberg autoionizing states in electric fields

V. L. Jacobs, J. Davis

Published Feb 1, 1979• 49 citations
Publisher

Abstract

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 $n$. 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 $l$. 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 ${\mathrm{Fe}}^{+23}$ ion through the $2p\ensuremath{\rightarrow}2s$ inner-electron transition, where the contributions from large-$n$ 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 $l$ substates substantially increases the autoionization rates from the higher-$l$ sublevels.

DOI
10.1103/physreva.19.776

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Effects of electric fields on doubly excited autoionizing Rydberg states of barium

Kambiz Ali Safinya, J. F. Delpech, Thomas F. Gallagher

We report the effects of static electric fields on the doubly excited $6{p}_{\frac{1}{2}}\mathrm{nl}$ states of barium in the region ${n}^{*}=12$. Using a three-step laser excitation scheme we have measured the electric-field dependence of the positions and autoionization widths of the $6{p}_{\frac{1}{2}}\ensuremath{-}17s,16p,15d,12l (l=4\ensuremath{-}10),12f, \mathrm{and} 16s$ states at field values of up to 4.92 kV/cm. The photoexcitation spectra of the autoionizing states exhibit interference effects which are well understood and provide a better understanding of the character of these states in electric fields. The systematic study of the spectra and positions allows us to explain the field dependence of the autoionization widths in terms of electric-field mixing of the discrete portions of the auoionizing states. The relationship of these effects to dielectronic recombination rates of ions and electrons in plasma microfields is discussed.

Physical Review A•Sep 1, 1980•20 citations

l dependence of dielectronic recombination from a continuum of finite bandwidth in a static electric field

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It should be possible to separate experimentally the contributions to dielectronic recombination (DR) of energetically unresolved intermediate autoionizing Rydberg $nl$ states using electric fields. This notion is based on two essential ideas. First, electric fields enhance the DR rate by Stark-mixing low-$l$ states with high autoionization rates with high-$l$ states with low autoionization rates. Second, the field at which an $l$ state becomes Stark mixed is determined by its quantum defect, a known function of $l$. Consequently, the electric-field dependence of the DR rate should reflect the $l$ dependence of the autoionization rates and thus the contributions of the zero-field $nl$ states to the DR rate. This notion cannot be tested experimentally by examining true DR. However, it can be tested by studying DR from a continuum of finite bandwidth (CFB), for in this case the intermediate Rydberg $nl$ states are restricted to a single value of $l$. Specifically, we have examined the electric-field dependence of DR from two CFB's, the $\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{p}_{3∕2}11d$ and $6{p}_{3∕2}8g$ states. In these two cases the intermediate autoionizing Rydberg states are restricted to the $\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{p}_{1∕2}nd$ and $6{p}_{1∕2}ng$ states $(l=2\phantom{\rule{0.5em}{0ex}}\text{and}\phantom{\rule{0.5em}{0ex}}4)$, which have quantum defects of 0.25 and 0.02, respectively. For the same $n$ they are Stark mixed at fields differing by an order of magnitude. We show experimentally that enhancement of the DR rate occurs at fields differing by a factor of 10 for $nd$ and $ng$ states of the same $n$, as expected, confirming that the field dependence of DR can be used to extract information about the contributions of energetically unresolved $l$ states to the zero-field DR rate.

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Autoionization of Rydberg states with large angular momentum: Application to alkaline-earth atoms

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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.

Physical Review A•Oct 1, 1988•51 citations
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→2s2p\ensuremath{\rightarrow}2s2p\ensuremath→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.
We report the effects of static electric fields on the doubly excited 6p12nl6{p}_{\frac{1}{2}}\mathrm{nl}6p21​​nl states of barium in the region n∗=12{n}^{*}=12n∗=12. Using a three-step laser excitation scheme we have measured the electric-field dependence of the positions and autoionization widths of the $6{p}_{\frac{1}{2}}\ensuremath{-}17s,16p,15d,12l (l=4\ensuremath{-}10),12f, \mathrm{and} 16s$ states at field values of up to 4.92 kV/cm. The photoexcitation spectra of the autoionizing states exhibit interference effects which are well understood and provide a better understanding of the character of these states in electric fields. The systematic study of the spectra and positions allows us to explain the field dependence of the autoionization widths in terms of electric-field mixing of the discrete portions of the auoionizing states. The relationship of these effects to dielectronic recombination rates of ions and electrons in plasma microfields is discussed.
It should be possible to separate experimentally the contributions to dielectronic recombination (DR) of energetically unresolved intermediate autoionizing Rydberg nlnlnl states using electric fields. This notion is based on two essential ideas. First, electric fields enhance the DR rate by Stark-mixing low-lll states with high autoionization rates with high-lll states with low autoionization rates. Second, the field at which an lll state becomes Stark mixed is determined by its quantum defect, a known function of lll. Consequently, the electric-field dependence of the DR rate should reflect the lll dependence of the autoionization rates and thus the contributions of the zero-field nlnlnl states to the DR rate. This notion cannot be tested experimentally by examining true DR. However, it can be tested by studying DR from a continuum of finite bandwidth (CFB), for in this case the intermediate Rydberg nlnlnl states are restricted to a single value of lll. Specifically, we have examined the electric-field dependence of DR from two CFB's, the Ba6p3∕211d\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{p}_{3∕2}11dBa6p3∕2​11d and 6p3∕28g6{p}_{3∕2}8g6p3∕2​8g states. In these two cases the intermediate autoionizing Rydberg states are restricted to the Ba6p1∕2nd\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{p}_{1∕2}ndBa6p1∕2​nd and 6p1∕2ng6{p}_{1∕2}ng6p1∕2​ng states (l=2and4)(l=2\phantom{\rule{0.5em}{0ex}}\text{and}\phantom{\rule{0.5em}{0ex}}4)(l=2and4), which have quantum defects of 0.25 and 0.02, respectively. For the same nnn they are Stark mixed at fields differing by an order of magnitude. We show experimentally that enhancement of the DR rate occurs at fields differing by a factor of 10 for ndndnd and ngngng states of the same nnn, as expected, confirming that the field dependence of DR can be used to extract information about the contributions of energetically unresolved lll states to the zero-field DR rate.
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.
This volume offers a timely look at Rydberg states of atoms in external fields and dielectronic recombination. Each topic provides authoritative coverage, presents a fresh account of a flourishing field of current atomic physics and introduces new opportunities for discovery and development. Topics considered include electron-atom scattering in external fields; observations of regular and irregular motion as exemplified by the quadratic zeeman effect and other systems; Rydberg atoms in external fields and the Coulomb geometry; crossed-field effects in the absorption spectrum of lithium in a magnetic field; precise studies of static electric field ionization; widths and shapes of stark resonances in sodium above the saddle point; studies of electric field effects and barium autoionizing resonances; autoionization and dielectronic recombination in plasma electric microfields; dielectronic recombination measurements on multicharged ions; merged beam studies of dielectronic recombination; Rydberg atoms and dielectronic recombination in astrophysics; and observations on dielectronic recombination.
The Stark spectra of autoionizing Rydberg states of Xe converging to the second ionization limit 5p5{p}^{5}p5 2P1/2^{2}P_{1/2}2P1/2​ have been investigated as a function of applied electric field over the range 26--2362 V/cm. Single-photon excitation from the Xe ground state was achieved using coherent radiation near 92.5 nm, generated by frequency tripling the pulsed output of a frequency-doubled dye laser in a free jet of rare-gas atoms. For the lowest electric field only the ns' and nd' series were observed. As the electric field was increased the np' series appeared because of the mixing of wave functions with different l values. Further increase of the electric field caused the appearance of hydrogenlike Stark manifolds. The Stark spectrum was simulated in a two-step procedure with no adjustable parameters. Using a jl-coupling basis set the Hamiltonian matrix was diagonalized to determine the energy levels and corresponding eigenfunctions for a given electric field strength. The intensities and line shapes were then calculated using the formalism developed by Fano for a many-discrete-level--single-continuum configuration interaction. This treatment was sufficient to reproduce the positions, widths, and shapes of most observed features. At field strengths between 1000 and 2000 V/cm, however, an additional modulation structure with a spacing of about 2.7 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ appeared on top of the \ensuremath{\Vert}M\ensuremath{\Vert}=1 autoionizing resonances, which could not be explained by our simple theoretical model.
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.