Three-body Recombination Rate Research Articles

Three Body Recombination of Ultracold Dipoles to Weakly Bound Dimers

We use universality in two-body dipolar physics to study three-body recombination. We present results for the universal structure of weakly bound two-dipole states that depend only on the s-wave scattering length (a). We study threshold three-body recombination rates into weakly bound dimer states as a function of the scattering length. A Fermi golden rule analysis is used to estimate rates for different events mediated by the dipole-dipole interaction and a phenomenological contact interaction. The three-body recombination rate in the limit where a≫D contains terms which scale as a{4}, a{2}D{2}, and D4, where D is the dipolar length. When a≪D, the three-body recombination rate scales as D4.

Magnetic-field dependence and Efimov resonance broadening in ultracold three-body recombination

We derive an analytic formula which describes the final bound state dependence in ultracold three-body recombination. Using an energy-dependent loss parameter, the recently observed broad resonance in an ultracold gas of $^{6}\mathrm{Li}$ atoms [T. B. Ottenstein, T. Lompe, M. Kohnen, A. N. Wenz, and S. Jochim, Phys. Rev. Lett. 101, 203202 (2008); J. H. Huckans, J. R. Williams, E. L. Hazlett, R. W. Stites, and K. M. O'Hara, Phys. Rev. Lett. 102, 165302 (2009)] is described quantitatively. We also provide an analytic and approximation for the three-body recombination rate which encapsulates the underlying physics of the universal three-body recombination process.

Time-resolved optical emission spectroscopy of laser-produced air plasma

Time-resolved optical emission spectroscopy (OES) is used to analyze a mesh-initiated air breakdown plasma induced by a transverse excitation atmospheric CO2 pulsed laser (λ=10.591 μm, 64 ns (full width at half maximum), 70–160 J/cm2). Emission from excited N, O, C, H, and Ar; ionic fragment N+, O+, N2+, O2+, C+, and molecular band systems of N2+(B Σ2u+−X Σ2g+; D Π2g−A Π2u), N2(C Π3u−B Π3g), and OH(A Σ2+−X Π2) is observed. Plasma characteristics are examined in detail on the emission lines of N+, O+, and C by time-resolved OES technique. The results show a faster decay of continuum and ionic spectral species than of neutral atomic and molecular ones. The velocity and kinetic energy distributions for the different species were obtained from time-of-flight measurements. Excitation temperature and electron density in the laser-induced plasma were estimated from the analysis of spectral data at various times from the laser pulse incidence. Temporal evolution of electron density has been used for the estimation of the three-body recombination rate constant.

Three Resonant Ultracold Bosons: Off-Resonance Effects

We solve a finite range two-channel model for three resonant identical bosons. The model provides a minimal description of the various magnetic Feshbach resonances in single species ultracold bosonic systems, including off-resonant scattering. We obtain important insights into the interpretation of seminal experiments: the three-body recombination rate measured in sodium and the Efimov resonances observed in cesium. This approach quantifies nonuniversal effects appearing for a finite magnetic field detuning.

Rydberg atom formation in ultracold plasmas: Non-equilibrium dynamics of recombination

Rydberg atom formation is a source of heating in plasmas. The rate of three-body recombination in an ultracold neutral plasma was measured and temperature for the plasma was extracted. With large-scale Monte Carlo and particle-in-cell simulations, we have ab initio calculated 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.

Rydberg atom formation in ultracold plasmas: Non-equilibrium dynamics of recombination

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.

Evidence for an Excited-State Efimov Trimer in a Three-Component Fermi Gas

We observe enhanced three-body recombination in a three-component ;{6}Li Fermi gas attributable to an excited Efimov trimer state intersecting the three-atom scattering threshold near 895 G. From measurements of the recombination rate we determine the Efimov parameters kappa_{*} and eta_{*} for the universal region above 600 G which includes three overlapping Feshbach resonances. The value of kappa_{*} also predicts the locations of loss features previously observed near 130 and 500 G [T. B. Ottenstein, Phys. Rev. Lett. 101, 203202 (2008)10.1103/PhysRevLett.101.203202; J. H. Huckans, Phys. Rev. Lett. 102, 165302 (2009)10.1103/PhysRevLett.102.165302] suggesting they are associated with a ground-state Efimov trimer near threshold. We also report on the realization of a degenerate three-component Fermi gas with approximate SU(3) symmetry.

Theoretical studies on dielectronic recombination of neonlike gold and its effects on plasma ionization balance and radiation energy

The dielectronic recombination (DR) of neonlike gold ions is investigated employing the flexible atomic code based on the relativistic configuration interaction method, and its influence on the ionization balance and radiation energy in high-temperature plasma is also studied. The total resonance strength for LMM configuration complex is in a good agreement with the experimental measurement and other theoretical works. The DR rate coefficients are calculated and compared with the three-body recombination and radiative recombination rate coefficients. The DR process is the dominant recombination mechanism of Ne-like gold ions for plasma with temperature Te≥6.5 keV and density ne≤2×1022 cm-3, which is close to the condition of X-ray conversion region in the inertial confinement fusion. Moreover, the DR satellite spectra of LMM, LMN and LMO resonances are simulated, and compared with the intensities of the corresponding resonance lines induced by the electron impact excitation. The intensity ratio of the satellite line 3D’ $[(2p^{5}_{3/2}3d_{3/2}3d_{5/2})_{J=5/2}$ – $(2p^{6}3d_{3/2})_{ J=3/2}]$ and the resonance line 3D $[(2p^{5}_{3/2}3d_{5/2})_{J=1}$ – $(2p^{6})_{J=0}]$ is given, which can be applied for diagnostics of plasma temperature.

Three-Body Recombination ofLi6Atoms with Large Negative Scattering Lengths

The three-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex-valued. We provide semianalytic expressions for the cases of 2 or 3 equal scattering lengths, and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of 6Li atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.

Confinement-induced Efimov resonances in Fermi-Fermi mixtures

A Fermi-Fermi mixture of $^{40}\text{K}$ and $^{6}\text{L}\text{i}$ does not exhibit the Efimov effect in a free space, but the Efimov effect can be induced by confining only $^{40}\text{K}$ in one dimension. Here the Efimov's three-body parameter is controlled by the confinement length. We show that the three-body recombination rate in such a system in the dilute limit has a characteristic logarithmic-periodic dependence on the effective scattering length with the scaling factor 22.0 and can be expressed by formulas similar to those for identical bosons in three dimensions. The ultracold mixture of $^{40}\text{K}$ and $^{6}\text{L}\text{i}$ in the one-dimensional--three-dimensional mixed dimensions is thus a promising candidate to observe the Efimov physics in fermions.

Dynamical formation and interaction of bright solitary waves and solitons in the collapse of Bose–Einstein condensates with attractive interactions

We model the dynamics of formation of multiple, long-lived, bright solitary waves (BSWs) in the collapse of Bose–Einstein condensates with attractive interactions as studied in the experiment of Cornish et al (2006 Phys. Rev. Lett. 96 170401). We use both mean-field and approximate quantum field simulation techniques. While a number of separated wave packets form as observed in the experiment, they do not have a repulsive π phase difference as has been previously inferred. We observe that the inclusion of quantum fluctuations causes soliton dynamics to be predominantly repulsive in one-dimensional (1D) simulations independent of their initial relative phase. However, indicative 3D simulations do not show a similar effect. In contrast, in 3D quantum noise has a negative impact on BSW lifetimes. Finally, we show that condensate oscillations, after the collapse, may serve to deduce three-body recombination rates.

Geometrical Phase Driven Predissociation: Lifetimes of22A′Levels ofH3

We discuss the role of the geometric phase in predissociation dynamics of vibrational states near a conical intersection of two electronic potential surfaces of a D{3h} molecule. We present a method to calculate lifetimes and positions of predissociated vibrational states (Feshbach resonances) for such X3 molecules. The method accounts for the two coupled three-body potential surfaces. As an example, the method is applied to obtain vibrational levels of the 2;{2}A' electronic state of H3. The three-body recombination rate coefficient for the H+H+H-->H{2}+H process is estimated.

Universal three-body dynamics in binary mixtures of ultra-cold atoms

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass m and the third particle of mass m 1 in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio m/m 1 and the total angular momentum L. For those L and m/m 1, which correspond to the finite number of vibrational states, all the binding energies are described by the universal function depending on two scaled variables. The detailed study is performed for L = 1; in particular, it is shown that a two-hump structure in the mass-ratio dependencies of the elastic scattering cross section and the three-body recombination rate are connected with arising of the bound states.

Collisional recombination in nonideal plasmas

We suggest a model that allows one to consider the kinetics of collisional recombination in a nonideal plasma and to calculate its rate by the molecular dynamics method. We have found that the dependence of the collisional recombination rate on the plasma coupling parameter differs significantly from the extrapolation of the three-body recombination rate to the nonideal region. The recombination rate in a strongly coupled plasma has been found to decrease with increasing coupling parameter. We have established that the effect of plasma nonideality increases with ion charge. The recombination kinetics is shown to depend significantly on how the ions are arranged in the medium. Collisional recombination transforms into three-body one as the coupling parameter of the medium decreases.

Three-body recombination of identical bosons with a large positive scattering length at nonzero temperature

For identical bosons with a large scattering length, the dependence of the three-body recombination rate on the collision energy is determined in the zero-range limit by universal functions of a single scaling variable. There are six scaling functions for angular momentum zero and one scaling function for each higher partial wave. We calculate these universal functions by solving the Skorniakov-Ter-Martirosian equation. The results for the three-body recombination as a function of the collision energy are in good agreement with previous results from solving the three-body Schr\"odinger equation for $^{4}\mathrm{He}$ atoms. The universal scaling functions can be used to calculate the three-body recombination rate at nonzero temperature. We obtain an excellent fit to the data from Grimm and co-workers for $^{133}\mathrm{Cs}$ atoms with a large positive scattering length.

Efimov states near a Feshbach resonance

We describe three-body collisions close to a Feshbach resonance by taking into account two-body scattering processes involving both the open and the closed channel. We extract the atom-dimer scattering length and the three-body recombination rate, predicting the existence at negative scattering length of a sharp minimum in the recombination losses due to the presence of a shallow bound level. We obtain very good agreement with the experimental results in atomic 133Cs of Kraemer et al. [Nature 440, 315 (2006)], and predict the position of Efimov resonances in a gas of 39K atoms.

Dielectronic Recombination of Sn10+ Ions and Related Satellite Spectra

Based on the multi-configuration Dirac–Fock method, theoretical calculations are carried out for the dielectronic recombination (DR) rate coefficients and the collision excitation rate coefficients of Sn10+ ions. It is found that the total DR rate coefficient has its maximum value between 10 eV and 100 eV and is greater than either the radiative recombination or three-body recombination rate coefficients (the number of free electrons per unit is 1021 cm3) for the case of Te > 1 eV. Therefore, DR can strongly influence the ionization balance of laser produced multi-charged tin ions. The related dielectronic satellite cannot be ignored at low temperature Te < 5 eV.

Recombination Dynamics of Metal Halides in the Presence of Vaporized Ferritic Steel

The Z-pinch driven fusion reactor will require extremely high current pulses to generate sufficient x-ray flux for the fusion target implosion. The fusion target is coupled to the pulsed power system through a recyclable transmission line (RTL) that is presently envisioned made of carbon steel. The energy released by the fusion pulse is absorbed by liquid flibe (Li2BeF4) coolant and by the RTL material which is partially vaporized and ionized. The objective of this paper is to characterize the recombination of vaporized metal halides in the presence of ferritic steel in a plasma with parameters similar to those expected in the Z-IFE chamber (plasma density < 2 x 1018 cm-3, Te < 40000 K). Using a substitute eutectic salt (Na2MgCl4) instead of flibe, we find experimentally that the three-body recombination rate of iron with chlorine is larger than that of sodium with chlorine. The measured recombination rates are compared to equilibrium recombination rates calculated at lower temperature (5000 K). The results suggest that an effective scheme for the removal of ferritic fluorite from the liquid flibe coolant may be needed in a Z-IFE reactor in addition to the mechanical separation of carbon steel RTL material required for recycling.

Calculations of recombination rates for coldHe4atoms from atom-dimer phase shifts and determination of universal scaling functions

Three-body recombination rates for cold $^4$He are calculated with a new method which exploits the simple relationship between the imaginary part of the atom-dimer elastic scattering phase shift and the $S$-matrix for recombination. The elastic phase shifts are computed above breakup threshold by solving a three-body Faddeev equation in momentum space with inputs based on a variety of modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII potential agree very well with the only previously published results. Since the elastic scattering and recombination processes for $^4$He are governed by "Efimov physics", they depend on universal functions of a scaling variable. The newly computed recombination coefficients for potentials other than HFD-B3-FCII make it possible to determine these universal functions for the first time.

Universality constraints on three-body recombination for cold atoms: FromHe4toCs133

For atoms with large scattering length, the dependence of the three-body recombination rate on the collision energy is determined by the scattering length and the Efimov three-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the three-body recombination rate for $^{4}\mathrm{He}$ atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the $^{4}\mathrm{He}$ results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to $^{133}\mathrm{Cs}$ atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.