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Physical Review Letters

Three-Body Recombination of Atomic Ions with Slow Electrons

S. X. Hu

Published Mar 29, 2007• 21 citations
Publisher

Abstract

Using the time-dependent wave-packets method, we have quantum mechanically investigated the three-body recombination process for electron energies varying from 10 to 0.01 eV. The classical "bottleneck" prediction on the probable population was confirmed by our S-wave quantum calculations for electron kinetic energies (K(E)) as low as 0.1 eV. But for K(E)<0.1 eV, the quantum three-body recombination tends to populate lower n levels than the classical theory predicted. We also find that, in the same n level, the recombination tends to populate higher angular-momentum states with K(E) decreasing. These results may shed light on the intrinsic dynamics of both ultracold plasmas and frozen Rydberg gases.

DOI
10.1103/physrevlett.98.133201

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Using the time-dependent wave-packets method, we have quantum mechanically investigated the three-body recombination process for electron energies varying from 10 to 0.01 eV. The classical "bottleneck" prediction on the probable population was confirmed by our S-wave quantum calculations for electron kinetic energies (K(E)) as low as 0.1 eV. But for K(E)<0.1 eV, the quantum three-body recombination tends to populate lower n levels than the classical theory predicted. We also find that, in the same n level, the recombination tends to populate higher angular-momentum states with K(E) decreasing. These results may shed light on the intrinsic dynamics of both ultracold plasmas and frozen Rydberg gases.
Inelastic n-changing collisions play an important role in the evolution of Rydberg atoms into ultracold plasmas. However, for the initially intermediate n (n ∼ 40) Rydberg states, these collisions can hardly be observed due to the low electron temperature in ultracold plasmas. In this work, we designed an experimental scheme to facilitate collisions between free electrons at 1.5 eV and intermediate n Rydberg atoms. Using the field ionization technique, we measured the state distributions resulting from the evolution of initially cold rubidium atoms in the 45P3/2 Rydberg state. The experimentally obtained probability of inelastic collisions excitation agrees well with the Monte Carlo simulation results. In addition, our experimental results indicate that the n-changing population induced by hot electrons is significant for lower nP Rydberg states. Our work plays a significant role in calculating the rates of electron-ion three-body recombination in ultracold plasmas.
In plasmas at very low temperatures, the formation of neutral atoms is dominated by collisional three-body recombination, owing to the strong $\ensuremath{\sim}{T}^{\ensuremath{-}9/2}$ scaling of the corresponding recombination rate with the electron temperature TTT. While this law is well established at high temperatures, the unphysical divergence as $T\ensuremath{\rightarrow}0$ clearly suggests a breakdown in the low-temperature regime. Here, we present a combined molecular dynamics Monte Carlo study of electron-ion recombination over a wide range of temperatures and densities. Our results reproduce the known behavior of the recombination rate at high temperatures, but reveal significant deviations with decreasing temperature. We discuss the fate of the kinetic bottleneck and resolve the divergence problem as the plasma enters the ultracold, strongly coupled domain.
Using state-selected double-resonant excitation, we create a Rydberg gas of NO molecules excited to the principal quantum number n = 50 of the f-series converging to the ion rotational level, N(+) = 2. This gas evolves to form an ultracold plasma, which expands under the thermal pressure of its electrons, and dissipates by electron-ion recombination. Under conditions chosen for this experiment, the observed rates of expansion vary with selected plasma density. Electron temperatures derived from these expansion rates vary from T(e) = 12 K for the highest density up to 16 K at four-fold lower density. Over this range, the apparent electron coupling parameter, defined as Γ(e) = e(2)/4πε(0)ak(B)T(e), falls from nearly three to about one. The decay of charged-particle density fits with a kinetic model that includes parallel paths of direct two-body and stepwise three-body dissociative recombination. The overall recombinative decay follows a second-order rate law, with an observed rate constant that fits with established scattering-theory estimates for elementary two-body dissociative recombination. A small residual increase in this rate constant with decreasing charged-particle density suggests a growing importance of the three-body recombination channel under conditions of decreasing electron correlation.
Ultracold neutral plasmas, created by photoionizing samples of laser-cooled atoms, have well-controlled initial density and temperature parameters. With initial particle peak densities of ~10^15 m^-3, initial ion temperatures in the tens of micro-Kelvin range, and initial electron temperatures with a controllable range of 1-1000 K, these systems provide a means to study otherwise laboratory-inaccessible parameter ranges for plasma research. Furthermore, these plasmas are inhomogeneous, unconfined, and freely expanding into a vacuum. Despite the extraordinarily low electron temperatures, the electron system remains weakly coupled, although the ion system exhibits strong coupling behavior. While the initial electron temperatures are very low in ultracold plasmas, the temperature evolution has only been measured indirectly, in the earliest ~5% of the plasma lifetime, and often with large uncertainties. We present a technique that, with further theoretical support, can provide straightforward temperature measurements throughout the first fifth of the plasma lifetime. By making use of collective modes of the plasma, we fit a model of Tonks-Dattner resonances (electron sound wave propagating in the plasma) to measurements of these resonances and obtain a time-dependent electron temperature measurement for the ultracold plasma. Three-body recombination, a plasma loss process that has a rate scaling with the -9/2 power of the electron temperature, is of obvious interest in these ultracold plasma systems. Several theoretical works have predicted that the three-body recombination rate expression would need to be modified at these low electron temperatures, although the validity of these changes often hinges on the electron system being strongly coupled. We have performed the lowest temperature measurements of three-body recombination rates in a plasma and show that these measurements potentially provide a low-uncertainty means to calculate electron temperatures.
Rydberg atom formation is a source of heating in plasmas. The rate of three-body recombination in an ultracold neutral plasma was measured and electron temperature was derived from it using standard equilibrium recombination rates. With large-scale Monte Carlo and particle-in-cell simulations, we have calculated ab initio the rate of excitation, de-excitation, ionization (and recombination) in electron-Rydberg atom collision and investigated the short-time dynamics of three-body recombination in an ultracold neutral plasma. Comparison with observed rates is quite good. Particular attention is paid to the low-frequency microfield effect on Rydberg state cut-off in the plasma.
Signals of ultracold plasma are observed by two-photon ionization of laser-cooled caesium atoms in a magneto-optical trap. Recombination of ions and electrons into Rydberg atoms during the expansion of ultracold plasma is investigated by using state-selective field ionization spectroscopy. The dependences of recombination on initial electron temperature (1–70 K) and initial ion density (∼10 10 cm −3 ) are investigated. The measured dependence on initial ion density is N 1.547+0.004 at a delay time of 5 μs. The recombination rate rapidly declines as initial electron temperature increases when delay time is increased. The distributions of Rydberg atoms on different values of principal quantum number n, i.e. n = 30–60, at an initial electron temperature of 3.3 K are also investigated. The main experimental results are approximately explained by the three-body recombination theory.