Three-body Recombination Rate Research Articles

Dipolar relaxation collisions in magnetically trapped7Li

We report the measurement of the rate constant for dipolar relaxation from the $(F=2,$ ${m}_{F}=2)$ hyperfine state of ${}^{7}\mathrm{Li}.$ The atoms are confined in a permanent magnet trap at a field of ${10}^{3} \mathrm{G}.$ The measured value of $(1.05\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14} {\mathrm{cm}}^{3}/\mathrm{s}$ agrees well with theory. Additionally, we determine an upper bound for the three-body molecular recombination rate constant of ${10}^{\ensuremath{-}27} {\mathrm{cm}}^{6}/\mathrm{s},$ which is also consistent with predictions.

Plasma Effects in Three-body Recombination of High-Z Bare Ions with Electrons

The influence of plasma effects on three-body recombination of bare ions with electrons in cold plasma in the electron cooler is discussed in context of recombination “enhancement” observed in storage ring experiments. We show that for high-Z bare ions and low electron temperatures and densities the cooler plasma becomes “nonideal”, leading to the enhancement of the three-body recombination rates. This effect is described in terms of the Debye screening length within the “rigid shift” approximation. We demonstrate, that in cold (T ≈ 1–10 K) anisotropic plasma the screening effect substantially enhances the three-body recombination rates for very high n-states. The relaxation of high Rydberg states below the field ionization cut-off, set in storage ring experiments, is discussed. The calculations are confronted with the experimental results obtained in storage ring experiments.

Spectrum analysis of three-body recombination rates for non-Maxwellian electron distributions under ultra-fast laser irradiation

Calculation of the three-body recombination rate is reformulated in a manner in which the velocity contribution is more explicit and the recombination rate is spectrum analysed for electron velocity distributions under ultra-fast laser irradiation. Electron distribution functions are calculated by using a two-dimensional Fokker-Planck simulation. The shape of the recombination rate spectrum with respect to the velocity is found to be well described by vf(v) where f(v) is the pitch-angle-averaged velocity distribution. It is shown visually that the increase in the slow electron population effectively enhances the recombination rate. The effect of a model energy loss on the recombination rate is also discussed.

Ionization and recombination rates of atomic oxygen in high-temperature air plasma flows

A nonlinear time-dependent collisional-radiative model for atomic oxygen is presented. Effective ionization and three-body recombination rate coefficients are calculated for either optically thin or thick plasmas where ${10}^{18}{\mathrm{m}}^{\mathrm{\ensuremath{-}}3}<~{n}_{e}<~{10}^{21}{\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$ and $8000\mathrm{K}<~{T}_{e}<~20000\mathrm{K}.$ In order to implement these coefficients easily in plasma flow codes, simple analytical expressions are proposed. Significant discrepancies with existing literature values are pointed out and discussed. The time-dependent approach confirms the importance of a quasi-steady-state condition to derive meaningful rate coefficients. Therefore the relaxation time necessary for the system to reach a quasi-steady-state limits the validity of the rate coefficients determined in this study. In optically thick cases, this relaxation time in either recombining or ionizing plasmas depends weakly on the electron temperature but strongly increases as the electron number density decreases. In optically thin cases, it is more difficult to derive general results since the relaxation time depends on the electron temperature, on densities, but also on the initial distribution on atomic levels.

Surprising rate coefficients for four isotopic variants of O+O2+M

Mass spectrometric analysis of nonequilibrium oxygen isotopic mixtures undergoing UV photolysis has been employed to study three-body recombination rate coefficients for the O+O2, Q+O2, O+Q2, and Q+Q2 (O=16O, Q=18O) reactions, all with M=80% N2:10% O2:10% Q2 at 200 Torr and 296 K. kO+O2 is in good agreement with the currently recommended value, while kQ+Q2 is only slightly smaller. Surprisingly, kQ+O2 is close to kO+O2, while kO+Q2 is ≈50% larger. As a consequence of this unusual behavior, kO+OQ must be ≈20% larger than kQ+OQ to produce the well-known enrichments that occur in the free atmosphere and in laboratory experiments involving scrambled mixtures. Contrary to what is usually assumed in discussions of the heavy ozone anomaly, these results indicate that isotopic asymmetry does not guarantee a rate coefficient advantage.

Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay

We have used three-body recombination rates as a sensitive probe of the statistical correlations between atoms in Bose-Einstein condensates (BEC) and in ultracold noncondensed dilute atomic gases. We infer that density fluctuations are suppressed in the BEC samples. We measured the three-body recombination rate constants for condensates and cold noncondensates from number loss in the ${F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$ hyperfine state of ${}^{87}\mathrm{Rb}$. The ratio of these is $7.4(2.6)$ which agrees with the theoretical factor of $3!$ and demonstrates that condensate atoms are less bunched than noncondensate atoms.

Plasma density effects on the three-body recombination rate coefficients

The existing reaction rate coefficients for the three-body recombination of ions with plasma electrons have a strong T −4.5 dependence on the electron temperature T, which seems to break down at low temperature, for T < 1 K ∼- 10 −4 eV. The obvious deficiency of the formula is the neglect of the plasma density effect on the recombined Rydberg states. A simple correctional procedure is adopted in terms of a density dependent cutoff of these high Rydberg states, which seems to improve the rates at low T. The total rate coefficients are now proportional to T −1, for the density N not too low. The T dependence is closely related to the density, so that the −4.5 exponent is still valid at high T and low N region. Some numerical examples are given, and possible further improvements are suggested. The high and low T formulas interpolate smoothly through the principal quantum number cutoffs.

Detection of oxygen atoms in a high pressure surfatron microwave discharge via two-photon four-wave mixing

PJ) oxygen atoms are detected in a high pressure surface wave discharge driven at 2.45 GHz via two-photon resonant degenerate four-wave mixing spectroscopy (TP-DFWM) in the forward folded BOX configuration. The nonlinear optical signal provides a direct measure of the relative oxygen atom concentration with high spatial resolution inside the discharge up to pressures of 1 bar and without distortions due to linear absorption or saturation effects. The axial distribution of oxygen atom concentration is observed to depend sensitively on total pressure and gas flux. For total gas pressures up to 600 mbar both in case of a mixture of 10% O2/He and 10% O2/Ar the concentration of oxygen atoms increases linearly with pressure. At higher pressures an increase with larger slope is observed for 10% O2/Ar, while the concentration remains constant for 10% O2/He. This is interpreted by an increase of the three-body recombination rate in O2/He mixtures.

Three-body recombination of ions with electrons in cooler-storage rings

Three-body recombination (TBR) of bare ions with free electrons of anisotropic velocity distribution is discussed in the context of recombination experiments in cooler-storage rings. The recombination rates are derived from the electron impact ionization rates using the modified Saha equation. Analytical expressions for the TBR rates and new scaling rules with main quantum number n, atomic number Z, and both transverse and longitudinal electron temperatures are derived for the low n-states regime probed in experiments in cooler-storage rings. In this context, the discrepancies found between measured rates and predictions for radiative recombination for the e + Ne10+ system [Gao et al., Phys. Rev. Lett. 75 (1995) 4381] are discussed. Present results show that TBR rates for the flattened electron beam velocity distribution cannot account for the recombination enhancement observed at very low relative energies.

Simulations of heating and electron energy distributions in optical field ionized plasmas.

The heating in underdense plasmas produced by optical field ionization and the resulting electron energy distributions have been calculated using Monte Carlo simulations. Though the magnitude of collisional heating is found to be low in plasmas with densities of interest for recombination x-ray lasers, the effect of electron-ion collisions on the shape of the electron energy distribution is important. The consequences that the calculated energy distributions have on three-body recombination rates are found to be dramatic.

Three-body recombination rate of atomic nitrogen in low-pressure plasma flows.

A nonlinear collisional-radiative model for atomic nitrogen has been developed in order to determine effective recombination and associated ionization coefficients for either optically thin or optically thick plasmas where ${10}^{18}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$\ensuremath{\leqslant}${\mathit{n}}_{\mathit{e}}$\ensuremath{\leqslant}${10}^{21}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$ and 2000 K\ensuremath{\leqslant}${\mathit{T}}_{\mathit{e}}$\ensuremath{\leqslant}12 000 K. A time-dependent approach confirms the importance of the quasi-steady-state condition to derive meaningful rate coefficients. In order to implement these coefficients in plasma flow codes, simple analytical expressions are proposed. Significant discrepancies with existing literature values are pointed out and discussed. In recombining conditions, the relaxation time necessary to reach the quasi-steady-state is calculated, and depends on the electron number density and on the electron temperature. This time limits the validity of the recombination coefficient, especially in optically thick cases. Finally, for practical applications, the number of levels in Saha-Boltzmann equilibrium at the quasi-steady-state is also examined. \textcopyright{} 1996 The American Physical Society.

Decay of trapped ultracold alkali atoms by recombination.

Using the knowledge of two-body collision properties that has recently become available, we estimate the three-body recombination rate for doubly-spin-polarized ultracold gas samples of $^{7}\mathrm{Li}$, $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$ on the basis of the Jastrow approximation. We find that only recombination leading to the formation of the highest two-body bound states is important. The rate for the highest bound level with zero angular momentum is found to increase strongly with the absolute value of the two-body scattering length. \textcopyright{} 1996 The American Physical Society.

Two- and Three-body Ion-Electron Recombination Rate Coefficients in Neon

The rates of recombination of electrons with Net ions over a wide range of pressure (1001000 Torr) and at temperatures of 133, 233 and 295 K were measured. Two- and three-body recombination processes were resolved. The observed two-body rate coefficient is lower than earlier reports. The three-body rate measured agrees well with predictions from Flarinery's modified theory by Bates for termolecular ion-electron recombination in a monatomic gas.

Development of a pure cryogenic positron plasma using a LINAC positron source

The development of a high density cryogenic pure positron plasma trap at the LLNL positron beam facility opens new possibilities for antihydrogen research. We discuss a planned measurement of the three-body collisional recombination rate in magnetized plasmas, a possible antihydrogen atomic beam experiment, and other applications of pure positron plasmas.

Numerical simulations of charge state distribution from a KrF laser-produced plasma

A calculation of the charge state distribution of the asymptotic evolution of a plasma produced by an ultraviolet laser has been carried out by coupling the results of a detailed two-dimensional hydrodynamic simulation of the creation and heating of the plasma to a simpler one-dimensional hydrodynamic code. The latter incorporates time-dependent ionization and recombination physics and is used to model the subsequent expansion and cooling of the plasma. The simulation results are compared to experimental charge state distributions obtained by using a single shot electrodynamic charge analyzer. The sensitivity of the results to the rate coefficients used for the recombination calculations was tested and the calculated distributions were found to be most sensitive to the values of the three-body recombination rate and the amount of heat returned to the plasma. Reasonable agreement was found between the measured and calculated charge state distributions.

Electron-ion three-body recombination coefficient of argon

Spectroscopic measurements of a 15-kW flowing argon plasma, produced by an atmospheric pressure radio frequency inductively coupled plasma torch, have been made. The plasma is found to be in partial local thermodynamic equilibrium at electronic levels as low as 4p. Ionizational nonequilibrium is observed in the form of an elevated electron density due to the finite three-body electron-ion recombination rate. The flowing plasma is modeled using a two-dimensional axisymmetric flow code, incorporating partial local thermodynamic equilibrium effects, radiative transfer, and ionizational nonequilibrium through the coupled electron continuity equation

Factors controlling the x-ray pulse emission from an intense femtosecond laser-heated solid.

The evolution and radiation of strongly heated and ionized solid density material is calculated for conditions which are produced by an intense, femtosecond laser pulse. It is found that the spectrally integrated radiation emitted in the frequency range h\ensuremath{\nu}&gt;${\mathit{kT}}_{\mathit{e}}$, where ${\mathit{T}}_{\mathit{e}}$ is the initial peak plasma temperature, can be as short in duration as \ensuremath{\sim}100 fs if ${\mathit{kT}}_{\mathit{e}}$ is in an optimum range, set by the target material chosen. For temperatures in this range, the radiation pulse duration is controlled primarily by hydrodynamic expansion. Low x-ray yields can be attributed to suppression of high-ion-stage populations by the high rate of three-body recombination in solid density plasma.

Guiding center atoms: Three-body recombination in a strongly magnetized plasma

The three-body recombination rate is calculated for an ion introduced into a magnetically confined, weakly correlated, and cryogenic pure electron plasma. The plasma is strongly magnetized in the sense that the cyclotron radius for an electron rce=(kBTe/me)1/2/Ωce is small compared to the classical distance of closest approach b=e2/kBTe, where Te is the electron temperature and Ωce=eB/mec is the electron cyclotron frequency. Since the recombination rate is controlled by a kinetic bottleneck a few kBTe below ionization, the rate may be determined by considering only the initial cascade through states of electron-ion pairs with separation of order b. These pairs may be described as guiding center atoms since the dynamics is classical and treatable with the guiding center drift approximation. In this paper, an ensemble of plasmas characterized by guiding center electrons and stationary ions is described with the BBGKY hierarchy. Under the assumption of weak electron correlation, the hierarchy is reduced to a master equation. Insight to the physics of the recombination process is obtained from the variational theory of reaction rates and from an approximate Fokker–Planck analysis. The master equation is solved numerically using a Monte Carlo simulation, and the recombination rate is determined to be 0.070(10)n2eveb5 per ion, where ne is the electron density and ve=(kBTe/me)1/2 is the thermal velocity. Also determined by the numerical simulation is the transient evolution of the distribution function from a depleted potential well about the ion to its steady state.

Calculations of rate constants for the three-body recombination of H2 in the presence of H2

We construct a new global potential energy hypersurface for H2+H2 and perform quasiclassical trajectory calculations using the resonance complex theory and energy transfer mechanism to estimate the rate of three-body recombination over the temperature range 100–5000 K. The new potential is a faithful representation of ab initio electronic structure calculations, is unchanged under the operation of exchanging H atoms, and reproduces the accurate H3 potential as one H atom is pulled away. Included in the fitting procedure are geometries expected to be important when one H2 is near or above the dissociation limit. The dynamics calculations explicitly include the motion of all four atoms and are performed efficiently using a vectorized variable-stepsize integrator. The predicted rate constants are approximately a factor of 2 smaller than experimental estimates over a broad temperature range.

Spin-Polarized Atomic Hydrogen in Very High Magnetic Fields

We report preliminary results from our effort to extend the study of spin-polarized atomic hydrogen in high magnetic fields up to 20 Tesla. Recombination lifetimes are analyzed to extract three-body recombination rates. Our results are compared to theoretical predictions for reduced recombination and thus lifetime enhancement above 14 Tesla. Our discussion places particular emphasis on assessing the feasability of observing Bose-Einstein condensation in the ultrahigh field regime.