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Physical Review A

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

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

Published Jun 1, 2004• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.69.063402

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Physical Review A•Aug 2, 2002•3 citations
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.
We report the results of a study of the effects of combined electric and magnetic fields on dielectronic recombination (DR) from a continuum of finite bandwidth. Specifically, we have examined the process $\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{p}_{3∕2}8g\ensuremath{\rightarrow}\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{p}_{1∕2}nk\ensuremath{\rightarrow}\mathrm{Ba}\phantom{\rule{0.3em}{0ex}}6{s}_{1∕2}nk+h\ensuremath{\nu}$ in the presence of electric fields from 0to7V∕cm0\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}7\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}0to7V∕cm and magnetic fields from 0to250G0\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}250\phantom{\rule{0.3em}{0ex}}\mathrm{G}0to250G. Our observations elucidate the requirements for magnetic field enhancement of the DR rate. In particular, they demonstrate that the magnetic coupling must be comparable not only to the electric field splitting of the intermediate autoionizing Rydberg states, but also to their decay rates.
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.
The presence of an electric field converts the intermediate autoionizing Rydberg $n\ensuremath{\ell}$ states, through which dielectronic recombination passes, into nknknk Stark states, which have autoionization and capture rates in excess of the radiative decay rates and contribute to dielectronic recombination. In zero field the high $\ensuremath{\ell}$ states do not contribute to dielectronic recombination, but the conversion to Stark states makes it possible and raises the dielectronic recombination rate. However, an electric field can also result in coupling to loss channels which locally reduce the dielectronic recombination rate. We have observed holes in the spectrum of dielectronic recombination from the Ba 6p3∕28g6{p}_{3∕2}8g6p3∕2​8g continuum of finite bandwidth via the intermediate 6p1∕2ng6{p}_{1∕2}ng6p1∕2​ng states. The holes appear when an electric field is applied, and we attribute them to interaction with rapidly decaying $6{p}_{3∕2}8\ensuremath{\ell}$ states, which diverts flux from dielectronic recombination.
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 $\ensuremath{\Delta}n=0,$ $\ensuremath{\Delta}m=1$ transitions of the autoionizing Rydberg-Stark states with the microwave field.
We report the enhancement of dielectronic recombination from a continuum of finite bandwidth in combined electric and magnetic fields. Specifically, we have examined the process Ba $6{p}_{3/2}8g\ensuremath{\rightarrow}6{p}_{1/2}ng\ensuremath{\rightarrow}6{s}_{1/2}ng+h\ensuremath{\nu}$ for $32\ensuremath{\le}n\ensuremath{\le}47$ in combined fields ranging from 0 to 7 V/cm and 0 to 250 G. The results demonstrate that it is the component of $B\ensuremath{\perp}E$ that leads to enhancement. The experimental results indicate that the B\mathit{B}B field coupling must exceed the radiative rate, the autoionization rate, and the Stark splitting of the intermediate autoionizing Rydberg states.
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.