Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Microwave-induced dielectronic recombination above the classical ionization limit in a static field

Cherice M. Evans, E. S. Shuman, Thomas F. Gallagher

Published Apr 29, 2003• 1 citation
Publisher

Abstract

The presence of a static electric field substantially enhances the dielectronic recombination (DR) rate below the classical field ionization limit and suppresses DR entirely above it. The addition of a small microwave field polarized orthogonally to the static field leads to a substantial DR signal above the classical ionization limit. We have examined DR from a continuum of finite bandwidth in static fields from 0 to 130 V/cm and with 8--11 GHz microwave fields of amplitudes up to 5 V/cm. We attribute the microwave-induced DR above the classical limit to the transfer of atoms by the microwave field from autoionizing the $m=0$ Rydberg intermediate states to higher m states. Since higher m states are more stable against field ionization, these states are more likely to decay radiatively to stable bound Stark states, thereby completing DR. This m-changing process most likely occurs by resonantly driving the $\ensuremath{\Delta}n=0,$ $\ensuremath{\Delta}m=1$ transitions of the autoionizing Rydberg-Stark states with the microwave field.

DOI
10.1103/physreva.67.043410

Related papers

Resonant Enhancement of Dielectronic Recombination by a Microwave Field

Victor Klimenko, Thomas F. Gallagher

We have observed dielectronic recombination of ${\mathrm{Ba}}^{+}$ and ${e}^{\ensuremath{-}}$ from a continuum of finite bandwidth in the presence of microwave fields of frequencies 8.08 and 12.05 GHz and amplitudes of up to 2 V/cm. There are sharp resonant enhancements when the microwave frequency matches the $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, 2, and 3 resonances of the intermediate autoionizing Rydberg states, and we attribute the enhancements to resonant microwave Stark $\ensuremath{\ell}$ mixing. The microwave field provides a simple and powerful way to enhance the recombination rate for incident electrons of a specific energy.

Physical Review Letters•Oct 16, 2000•13 citations

Electric-field enhancement of dielectronic recombination from a continuum of finite bandwidth

J. G. Story, Brendan J. Lyons, Thomas F. Gallagher

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.

Physical Review A•Mar 1, 1995•25 citations

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

E. S. Shuman, C. Evans, Thomas F. Gallagher

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.

Physical Review A•Jun 1, 2004•3 citations

Resonant enhancement of dielectronic recombination from a continuum of finite bandwidth

Victor Klimenko, Thomas F. Gallagher

Dielectronic recombination of Ba from a continuum of finite bandwidth in microwave fields of 4, 8, and 12 GHz exhibits a resonant enhancement when the microwave frequency matches a $\ensuremath{\Delta}n=1,$ 2, or 3 transition in the intermediate autoionizing $n\mathcal{l}$ Rydberg states. The origin of the enhancement is resonant Stark mixing of high- and low-l states of different n. Surprisingly, there is little difference between linear and circular polarization of the microwave field, which is attributed to the fact that more than two n levels are coupled in both cases. The dependence of the widths of the resonances on the microwave field is related to how many n states are coupled, and the threshold field for the appearance of the resonances is due to the requirement that low-l states with nonzero quantum defects be mixed with the hydrogenic high-l states. Finally, recombination has been observed from energies in excess of the ${\mathrm{Ba}}^{+}$ ${6p}_{1/2}$ limit.

Physical Review A•Aug 2, 2002•3 citations

Resonant enhancement of dielectronic recombination by a high-frequency microwave field

E. S. Shuman, Thomas F. Gallagher

Dielectronic recombination via the Ba $6{p}_{3∕2}n\ensuremath{\ell}$ states from a continuum of finite bandwidth is resonantly enhanced by a 38.8-GHz microwave field at the energies for which the $\ensuremath{\Delta}n=1,\phantom{\rule{0.2em}{0ex}}2,\phantom{\rule{0.2em}{0ex}}\dots{},\phantom{\rule{0.2em}{0ex}}k$ transitions of the intermediate $6{p}_{1∕2}n\ensuremath{\ell}$ states are resonant with the microwave frequency. The mechanism is resonant Stark mixing of high and low $\ensuremath{\ell}$ states by the microwave field. While static field enhancement of dielectronic recombination occurs at fields scaling as ${n}^{\ensuremath{-}5}$, the field required for enhancement of the $\ensuremath{\Delta}n=k,\phantom{\rule{0.2em}{0ex}}k\ensuremath{\geqslant}2$ resonances is roughly $n$ independent.

Physical Review A•Mar 24, 2005•0 citations

Enhancement of dielectronic recombination by an electric field

Lung Ko, Victor Klimenko, Thomas F. Gallagher

Dielectronic recombination from a continuum of finite bandwidth has been examined down to very low electric fields, 60 mV/cm, with very high resolution. A tunable laser is used to excite atoms to the continuum of finite bandwidth, the broad $\mathrm{Ba} {6p}_{3/2}11d$ autoionizing state, which straddles the ${\mathrm{Ba}}^{+} {6p}_{1/2}$ limit. Atoms which make transitions into the high-lying $\mathrm{Ba} {6p}_{1/2}\mathrm{nd}$ states and radiatively decay to the bound $6snd$ states are detected by field ionization. The recombination, integrated over energy, has been measured for fields from 60 mV/cm to 28 V/cm, showing a peak at 0.5 V/cm, in agreement with expectation based on calculations done for other systems. The final-state distribution has been measured, showing that the outer electron remains a spectator in the radiative decay. At fields below 1.0 V/cm and binding energies less than 12 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the ${\mathrm{Ba}}^{+} {6p}_{1/2}$ limit we find a deviation of our experimental results from the isolated resonance approximation.

Physical Review A•Mar 1, 1999•18 citations
The presence of a static electric field substantially enhances the dielectronic recombination (DR) rate below the classical field ionization limit and suppresses DR entirely above it. The addition of a small microwave field polarized orthogonally to the static field leads to a substantial DR signal above the classical ionization limit. We have examined DR from a continuum of finite bandwidth in static fields from 0 to 130 V/cm and with 8--11 GHz microwave fields of amplitudes up to 5 V/cm. We attribute the microwave-induced DR above the classical limit to the transfer of atoms by the microwave field from autoionizing the m=0m=0m=0 Rydberg intermediate states to higher m states. Since higher m states are more stable against field ionization, these states are more likely to decay radiatively to stable bound Stark states, thereby completing DR. This m-changing process most likely occurs by resonantly driving the \ensuremathΔn=0,\ensuremath{\Delta}n=0,\ensuremathΔn=0, \ensuremathΔm=1\ensuremath{\Delta}m=1\ensuremathΔm=1 transitions of the autoionizing Rydberg-Stark states with the microwave field.
We have observed dielectronic recombination of Ba+{\mathrm{Ba}}^{+}Ba+ and ${e}^{\ensuremath{-}}$ from a continuum of finite bandwidth in the presence of microwave fields of frequencies 8.08 and 12.05 GHz and amplitudes of up to 2 V/cm. There are sharp resonant enhancements when the microwave frequency matches the $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, 2, and 3 resonances of the intermediate autoionizing Rydberg states, and we attribute the enhancements to resonant microwave Stark $\ensuremath{\ell}$ mixing. The microwave field provides a simple and powerful way to enhance the recombination rate for incident electrons of a specific energy.
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.
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.
Dielectronic recombination of Ba from a continuum of finite bandwidth in microwave fields of 4, 8, and 12 GHz exhibits a resonant enhancement when the microwave frequency matches a $\ensuremath{\Delta}n=1,$ 2, or 3 transition in the intermediate autoionizing nln\mathcal{l}nl Rydberg states. The origin of the enhancement is resonant Stark mixing of high- and low-l states of different n. Surprisingly, there is little difference between linear and circular polarization of the microwave field, which is attributed to the fact that more than two n levels are coupled in both cases. The dependence of the widths of the resonances on the microwave field is related to how many n states are coupled, and the threshold field for the appearance of the resonances is due to the requirement that low-l states with nonzero quantum defects be mixed with the hydrogenic high-l states. Finally, recombination has been observed from energies in excess of the Ba+{\mathrm{Ba}}^{+}Ba+ 6p1/2{6p}_{1/2}6p1/2​ limit.
Dielectronic recombination via the Ba $6{p}_{3∕2}n\ensuremath{\ell}$ states from a continuum of finite bandwidth is resonantly enhanced by a 38.8-GHz microwave field at the energies for which the $\ensuremath{\Delta}n=1,\phantom{\rule{0.2em}{0ex}}2,\phantom{\rule{0.2em}{0ex}}\dots{},\phantom{\rule{0.2em}{0ex}}k$ transitions of the intermediate $6{p}_{1∕2}n\ensuremath{\ell}$ states are resonant with the microwave frequency. The mechanism is resonant Stark mixing of high and low $\ensuremath{\ell}$ states by the microwave field. While static field enhancement of dielectronic recombination occurs at fields scaling as ${n}^{\ensuremath{-}5}$, the field required for enhancement of the $\ensuremath{\Delta}n=k,\phantom{\rule{0.2em}{0ex}}k\ensuremath{\geqslant}2$ resonances is roughly nnn independent.
Dielectronic recombination from a continuum of finite bandwidth has been examined down to very low electric fields, 60 mV/cm, with very high resolution. A tunable laser is used to excite atoms to the continuum of finite bandwidth, the broad Ba6p3/211d\mathrm{Ba} {6p}_{3/2}11dBa6p3/2​11d autoionizing state, which straddles the Ba+6p1/2{\mathrm{Ba}}^{+} {6p}_{1/2}Ba+6p1/2​ limit. Atoms which make transitions into the high-lying Ba6p1/2nd\mathrm{Ba} {6p}_{1/2}\mathrm{nd}Ba6p1/2​nd states and radiatively decay to the bound 6snd6snd6snd states are detected by field ionization. The recombination, integrated over energy, has been measured for fields from 60 mV/cm to 28 V/cm, showing a peak at 0.5 V/cm, in agreement with expectation based on calculations done for other systems. The final-state distribution has been measured, showing that the outer electron remains a spectator in the radiative decay. At fields below 1.0 V/cm and binding energies less than 12 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the Ba+6p1/2{\mathrm{Ba}}^{+} {6p}_{1/2}Ba+6p1/2​ limit we find a deviation of our experimental results from the isolated resonance approximation.