Three-body Collisions Research Articles

Possible Efimov Trimer State in a Three-Hyperfine-Component Lithium-6 Mixture

We consider the Efimov trimer theory as a possible framework to explain recently observed losses by inelastic three-body collisions in a three-hyperfine-component ultracold mixture of lithium 6. Within this framework, these losses would arise chiefly from the existence of an Efimov trimer bound state below the continuum of free triplets of atoms, and the loss maxima (at certain values of an applied magnetic field) would correspond to zero-energy resonances where the trimer dissociates into three free atoms. Our results show that such a trimer state is indeed possible given the two-body scattering lengths in the three-component lithium mixture and gives rise to two zero-energy resonances. The locations of these resonances appear to be consistent with observed losses.

Three-Body Dynamics in Single Ionization of Atomic Hydrogen by 75 keV Proton Impact

Doubly differential cross sections for single ionization of atomic hydrogen by 75 keV proton impact have been measured and calculated as a function of the projectile scattering angle and energy loss. This pure three-body collision system represents a fundamental test case for the study of the reaction dynamics in few-body systems. A comparison between theory and experiment reveals that three-body dynamics is important at all scattering angles and that an accurate description of the role of the projectile-target-nucleus interaction remains a major challenge to theory.

Observation of Heteronuclear Atomic Efimov Resonances

Building on the recent experimental observation with ultracold atoms, we report the first experimental evidence of Efimov physics in a heteronuclear system. A mixture of ;{41}K and ;{87}Rb atoms was cooled to few hundred nanokelvins and stored in an optical dipole trap. Exploiting a broad interspecies Feshbach resonance, the losses due to three-body collisions were studied as a function of the interspecies scattering length. We observe an enhancement of the three-body collisions for three distinct values of the interspecies scattering lengths, both positive and negative, where no Feshbach resonances are expected. We attribute the two features at negative scattering length to the existence of two kinds of Efimov trimers, KKRb and KRbRb.

Repulsive Fermi gas in a harmonic trap: Ferromagnetism and spin textures

We study ferromagnetism in a repulsively interacting two-component Fermi gas in a harmonic trap. Within a local density approximation, the two components phase-separate beyond a critical interaction strength, with one species having a higher density at the trap center. We discuss several easily observable experimental signatures of this transition. The mean field release energy, its separate kinetic and interaction contributions, as well as the potential energy, all depend on the interaction strength and contain a sharp signature of this transition. In addition, the conversion rate of atoms to molecules, arising from three-body collisions, peaks at an interaction strength just beyond the ferromagnetic transition point. We then go beyond the local density approximation, and derive an energy functional which includes a term that depends on the local magnetization gradient and acts as a `surface tension'. Using this energy functional, we numerically study the energetics of some candidate spin textures which may be stabilized in a harmonic trapping potential at zero net magnetization. We find that a hedgehog state has a lower energy than an `in-out' domain wall state in an isotropic trap. Upon inclusion of trap anisotropy we find that the hedgehog magnetization profile gets distorted due to the surface tension term, this distortion being more apparent for small atom numbers. We estimate that the magnetic dipole interaction does not play a significant role in this system. We consider possible implications for experiments on trapped Li-6 and K-40 gases.

Generalizations of the Fock and Kato expansions to systems of three quantum particles

The Schrodinger and Faddeev approaches to the solution of the problem of three quantum particles in the configuration space are used and developed in this review. Various methods for construction of generalizations of the Fock and Kato expansions to central or noncentral pair interactions of a more general type than Coulomb potentials are described and compared within the approaches in question. Emphasis is placed on the use of these generalizations for quantum-mechanical and numerical analysis of the structure of three-body wave functions and their Faddeev components near the two-body and three-body collision points and in the limit of the linear three-body configuration.

Calculation of resonances in the H+H2 reaction using the faddeev-AGS method

The H+H2 reactive collision is described quantum mechanically in terms of valence–bond electronic states and the Faddeev–AGS equations for three-body collisions. The permutational symmetry of identical nuclei is considered within the present approach, which appears to avoid some of the difficulties associated with the use of electronically adiabatic states. A procedure based on the eigenvalue analysis of the K-matrix is used to locate resonances. Calculations probing the energy region of the lowest resonance in the H3 system revealed one with an energy in good agreement with previous work.

Experiments on small (H2)N clusters

The nucleation process of small hydrogen clusters has been studied in detail with space, time, and number size resolution on the basis of supersonic expansions of the gas through a cryogenic nozzle operating in the thermal range 24 < T <110 K. The diagnostic of the jet medium is based on high sensitivity (few photons/sec) Raman spectroscopy with very high spatial resolution (\(\approx 2~\mu\)m), enabling for quantitative measurements with time resolution in the domain of nanoseconds. Temperatures down to 0.1 K have been attained in the jet at a collisional rate low enough to avoid sudden freezing of the gas. Clusters between two and eight molecular units are observed size-resolved. Features of the ortho-ortho and ortho-para hydrogen dimers, and the role of three-body collisions for nascent dimers and trimers are reported.

Revisiting Anomalous Diffusion Due To Molecular Crowding

Molecular diffusion is called anomalous when the mean-squared displacement of a moving particle does not increase linearly with time. Several simulation works demonstrated anomalous diffusion, as opposed to normal (i.e., Brownian) diffusion, in crowded environments with fixed and/or mobile obstacles. Experimental measurements often report a reduction of molecular diffusion but not necessarily anomalous diffusion in the cytoplasm. Here we propose two possible reasons for the discrepancy between simulations and experiments on diffusion in crowded environments. First, some of the previously developed algorithms might not accurately simulate three-body or higher order molecular collisions in the crowded environment. To this end, we have developed an event-driven, exact collision detection algorithmic scheme and systematically studied the impact of crowding on molecular diffusion. When these higher-order collisions are explicitly taken into account, the anomalous diffusion in 3D seen with the previously developed algorithms becomes less prominent or disappears. Second, experimental analyses that suggested anomalous diffusion might have been problematic. This is particularly relevant to fluorescence correlation spectroscopy (FSC). Unlike single-particle tracking (SPT), FCS does not provide direct information about trajectories of individual molecules. It relies on the analysis of fluctuations in the number of fluorescent particles in a focused laser spot. The diffusion of molecule is inferred from the shape of the autocorrelated fluorescent signals fitted to a mathematical formula purportedly representing anomalous diffusion. However, the latter formula was derived from a modified diffusion equation, which may not have physical basis, thus leading to potentially erroneous data analysis. We propose a new FCS autocorrelation formula based on continuous time random walk theory and fractional diffusion equation. Finally, we use this new FCS formula and the novel event-driven algorithm to simulate diffusion in crowded environments and discuss possible reconciliation of discrepancies between previous simulations and experimental data.

Feshbach resonances in an ultracoldLi7andRb87mixture

We report on the observation of five Feshbach resonances in collisions between ultracold $^{7}\mathrm{Li}$ and $^{87}\mathrm{Rb}$ atoms in the absolute ground-state mixture where both species are in their $\ensuremath{\mid}f,{m}_{f}⟩=\ensuremath{\mid}1,1⟩$ hyperfine states. The resonances appear as trap losses for the $^{7}\mathrm{Li}$ cloud induced by inelastic heteronuclear three-body collisions. The magnetic field values where they occur are important quantities for an accurate determination of the interspecies interaction potentials. Results of coupled channels calculations based on the observed resonances are presented and refined potential parameters are given. A very broad Feshbach resonance centered around $649\phantom{\rule{0.3em}{0ex}}\mathrm{G}$ should allow for fine-tuning of the interaction strength in future experiments.

The study of VUV emissions of Ar*2 excimers using three-photon absorption laser-induced fluorescence

The VUV emissions of the second continuum of argon at ∼130 nm were investigated for pressures ranging from 100 to 600 Torr after selectively populating the resonant atomic state of the 3p54s configuration of argon by using three-photon absorption laser-induced fluorescence. For brief and selective excitation conditions, a kinetic study was performed by analysing the VUV postluminescence decay of argon. This study clearly shows that only three-body collisions lead to the formation of the excimer Ar2(A1u). The three-body decay rate constant of the metastable state Ar4s[3/2]02 was measured for the first time under selective excitation (k′3 = (19.5 ± 2.1) Torr−2 s−1). The role of the first resonant and metastable states of argon in the formation of excimers responsible for the VUV emissions is discussed. A kinetic scheme showing the main reaction processes is proposed and compared with those already obtained with other rare gases.

Bose–Einstein condensates in optical lattices: the cubic–quintic nonlinear Schrödinger equation with a periodic potential

The cubic–quintic nonlinear Schrödinger equation with a periodic potential, which is expressed in terms of the Jacobian function dn, is used to model a Bose–Einstein condensate trapped in an optical lattice (in most cases, the dn potential is very close to the ordinary sinusoidal one). The quintic term in the equation represents either effects of three-body collisions (which is relevant in the case when the ordinary two-body collisions are very weak), or an effective deviation of the trapped condensate from the one-dimensionality. The cases of both repulsive and attractive two-body interactions are considered. The same model governs the planar propagation of light in waveguides with the cubic–quintic optical nonlinearity, the periodic potential being induced by transverse modulation of the refractive index. In the case of the attractive quintic term (which is always the case if it accounts for the residual non-one-dimensionality of the tightly trapped condensate), a new family of exact periodic solutions is constructed in terms of Jacobian elliptic functions. Using semi-analytical and numerical methods, a stability region for these periodic states is identified. The effect of boundaries is shown to be very weak.E Kengne dedicates this work to Taa Bah Deffo Takotue Innocent, the Chairman of the Bandjoun Community in Douala (Cameroon).

STUDYING DIQUARK STRUCTURE OF HEAVY BARYONS IN RELATIVISTIC HEAVY ION COLLISIONS

We propose the enhancement of Λc yield in heavy ion collisions at RHIC and LHC as a novel signal for the existence of diquarks in the strongly coupled quark-gluon plasma produced in these collisions as well as in the Λc. Assuming that stable bound diquarks can exist in the quark-gluon plasma, we argue that the yield of Λc would be increased by two-body collisions between [ud] diquarks and c quarks, in addition to normal three-body collisions among u, d and c quarks. A quantitative study of this effect based on the coalescence model shows that including the contribution of diquarks to Λc production indeed leads to a substantial enhancement of the Λc/D ratio in heavy ion collisions.

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.

Formation of antihydrogen in three-body antiproton-positron collisions

A quantum-mechanical approach is proposed for the formation of antihydrogen $(\overline{H})$ in the ground and excited states $(2s,2p)$ via the mechanism of three-body recombination (TBR) inside a trapped plasma of antiprotons $(\overline{p})$ and positrons $({e}^{+})$ or in the collision between the two beams of them. Variations of the differential as well as the total formation cross sections are studied as a function of the incident energies of both the active and the spectator ${e}^{+}$'s. Significantly large cross sections are found at very low incident energies in the TBR process as compared to other processes leading to antihydrogen. The present $(\overline{H})$ formation cross section decreases with increasing positron energy (temperature) but no simple power law could be predicted for it covering the entire energy range $(\ensuremath{\sim}5--50\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$, corroborating the experimental findings qualitatively, the latter being at a much lower energy regime $(\ensuremath{\sim}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$. The formation cross sections are found to be much higher for unequal energies of the two ${e}^{+}$'s than for equal energies, as expected physically.

Three-body collisions in a plasma in a strong laser field

Electron-ion collisions in a high-density plasma in strong electromagnetic fields are considered. The applicability condition for the approximate model of pair collisions in strong fields are determined. It is shown that this condition is identical to the condition for the plasma to be transparent. Investigations were carried out by the test particle method generalized to the case of several scattering centers. An accurate calculation of short-range collisions is provided by a “jump” method that is based on the exact solution to the problem of the motion of a particle in a Coulomb potential. This method can also be applied in other approaches to simulating a collisional plasma (such as particle-in-cell and molecular dynamics methods).

Alternative paths to observing Efimov physics

We present some of our work on the ultracold behavior of three-body collisions and their relation to the recent experiment (Kraemer [1]). In particular, we discuss the role of Efimov physics in this experiment and other ultracold three-body collisions. We also suggest one way to make observation of the key feature of the Efimov effect – geometrical scaling – more experimentally feasible.

ΛcEnhancement from Strongly Coupled Quark-Gluon Plasma

We propose the enhancement of Lambdac as a novel quark-gluon plasma signal in heavy ion collisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider. Assuming a stable bound diquark state in the strongly coupled quark-gluon plasma near the critical temperature, we argue that the direct two-body collision between a c quark and a [ud] diquark would lead to an enhanced Lambdac production in comparison with the normal three-body collision among independent c, u, and d quarks. In the coalescence model, we find that the Lambdac/D yield ratio is enhanced substantially due to the diquark correlation.

Spatio-Temporal Effect of Gas Pressure on Excited Xe Atoms in Ultrafine Pixel Pitch AC Plasma Display Panels

The kaleidoscopic change in the distributions of excited xenon (Xe) atom density was investigated under a high gas pressure condition in a unit microdischarge cell on a coplanar-structured alternating-current plasma display panel with an ultrafine pixel pitch by using microscopic laser absorption spectroscopy. As the gas pressure increased, the peak densities of the excited atoms not only increased but the peak position on the anode side also tended to shift toward the center of the discharge gap by expanding in width. The temporal behavior of the excited Xe atom density in the resonant state (1s4) did not change significantly with the pressure since the decay rate was mostly governed by the effective lifetime of the imprisoned resonance radiation. On the contrary, the decay rate of the excited Xe atoms in the metastable state (1s5) decreased drastically with the pressure due to an increase in the three-body collision rate. This implied that the metastable state atoms were efficiently converted to Xe excimers, leading to an increase in the vacuum ultraviolet emission.

Breakdown of Integrability in a Quasi-1D Ultracold Bosonic Gas

We demonstrate that virtual excitations of higher radial modes in an atomic Bose gas in a tightly confining waveguide result in effective three-body collisions that violate integrability in this quasi-one-dimensional quantum system and give rise to thermalization. The estimated thermalization rates are consistent with recent experimental results in quasi-1D dynamics of ultracold atoms.

Application of exterior complex scaling to positron-hydrogen collisions including rearrangement

The application of an exterior complex scaling method to an atomic scattering problem with distinct rearrangement channels is reported. Calculations are performed for positron-hydrogen collisions in an s -wave model employing an electron-positron potential of V12 =- [8+ (r1 - r2) 2] -1/2, using the time-independent propagating exterior complex scaling method. This potential has the correct long-range Coulomb tail of the full problem and the results demonstrate that exterior-complex-scaling-based methods can accurately calculate scattering, ionization,and positronium formation cross sections in this three-body rearrangement collision.