We investigate three-body recombination rates into deep dimers in cold atomic gases with large scattering length within hyper-spherical adiabatic zero-range approach. We derive closed analytic expressions for the rates for one- and two-species gases. Although the deep dimers are beyond the zero-range theory the latter can still describe the recombination into deep dimers by use of one additional short-range absorption parameter. The recombination rate, as function of the scattering length, retains the known universal behavior --- the fourth power trend with characteristic log-periodic peaks --- however increasing the short-range absorption broadens the peaks until they are eventually completely smeared out. Increasing the heavy-to-light mass ratio in a two-species system decreases the distance between the peaks and increases the overal scale of the recombination rate.
The dimer-atom-atom recombination process in the system of four identical bosons with resonant interactions is studied. The description uses the exact Alt, Grassberger and Sandhas equations for the four-particle transition operators that are solved in the momentum-space framework. The dimer-dimer and atom-trimer channel contributions to the ultracold dimer-atom-atom recombination rate are calculated. The dimer-atom-atom recombination rate greatly exceeds the three-atom recombination rate.
We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering len…
Recent theoretical developments in the four-boson system with resonant interactions are described. Momentum-space scattering equations for the four-particle transition operators are used. The properties of unstable tetramers with approximate dimer-atom-atom structure are determined. In addition, the three- and four-cluster recombination processes in the four-boson system are studied.
In the systems of spin $\frac12$ fermions with resonant $S$-wave interactions supporting only weakly bound dimers the antisymmetry forbids recombination of three (or more) fermions at zero energy. However, the fermion-fermion-dimer recombination is only partially suppressed. It is studied in the framework of momentum-space integral equations for the four-particle transition operators. In the vicinity of the unitary limit the fermion-fermion-dimer recombination rate, rescaled to build dimensionless quantity, is found to be linear in the effective range parameter, enabling a simple and accurate …
This paper reports results from an experimental investigation of the dissociative recombination (DR) of the helium dimer ions at the heavy-ion Test Storage Ring (TSR) in Heidelberg, observing neutral products from electron-ion collisions in a merged beams configuration at relative energies from near-zero (thermal electron energy about 10 meV) up to 40 eV.
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 $a\gg D$ contains terms which scale as $a^{4…
For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body s-wave dimer, there exists an infinite number of three-body bound states. This effect is the well-known Efimov effect. These three-body states (Efimov states) are found to be universal for ultracold atomic gases and the lowest Efimov state crosses the three-body break-up threshold when the s-wave two-body scattering length is $a \approx -9.73 r_{\rm vdW}$, $r_{\rm vdW}$ being the van der Waals length. This article focuses on a generalized version of this Efimov scenario…
A universal dimer is subject to secondary collisions with atoms when formed in a cloud of ultracold atoms via three-body recombination. We show that in a collisionally opaque medium, the value of the scattering length that results in the maximum number of secondary collisions may not correspond to the Efimov resonance at the atom-dimer threshold and thus can not be automatically associated with it. This result explains a number of controversies in recent experimental results on universal three-body states and supports the emerging evidence for the significant finite range corrections to the fi…
We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three-body recombination rate $K_3$ where three free atoms interact to produce an atom--dimer pair, and the relaxation rate $K_{\rm rel}$ where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for $K_3$, namely the NTR (Near Threshold Resonance) regime behavior $E^{-2}$ for negative scattering lengths and the NTS (Near Threshold Supp…
A very recently method for classical trajectory calculations for three-body collision [J. Pérez-Ríos, S. Ragole, J. Wang and C. H. Greene, J. Chem. Phys. {\bf 140}, 044307 (2014)] has been applied to describe ion-neutral-neutral ternary processes for low energy collisions: 0.1 mK - 10 mK. As a result, a threshold law for the three-body recombination cross section is obtained and corroborated both, experimentally and numerically. The derived threshold law predicts the formation of weakly bound dimers, with binding energies comparable to the collision energy of the collisional partners. In this …
We calculate the three-body recombination rate into a shallow dimer in a gas of cold bosonic atoms near a Feshbach resonance using a two-channel contact interaction model. The two-channel model naturally describes the variation of the scattering length through the Feshbach resonance and has a finite effective range. We confront the theory with the available experimental data and show that the two-channel model is able to quantitatively describe the existing data. The finite effective range leads to a reduction of the scaling factor between the recombination minima from the universal value of 2…
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 $^4$H…
We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $α\approx 67.1\sin^2[s_0\ln(κ_*a)+γ]$, for different values of $a$ and selected values of the three-body parameter $κ_*$. A g…
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 $^{6}$Li atoms [T. B. Ottenstein {\it et al.}, Phys. Rev. Lett. 101, 203202 (2008)l J. H. Huckans {\it et al.}, 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.
We present improved fits to our treatment of suppression of dielectronic recombination at intermediate densities. At low densities, most recombined excited states eventually decay to the ground state, and therefore the total dielectronic recombination rate to all levels is preserved. At intermediate densities, on the other hand, collisions can lead to ionization of higher-lying excited states, thereby suppressing the dielectronic recombination rate. The improved suppression factors presented here, although highly approximate, allow summed recombination rate coefficients to be used to intermedi…
A formula for the cross section and event rate constant describing recombination of N particles are derived in terms of general S-matrix elements. Our result immediately yields the generalized Wigner threshold scaling for the recombination of N bosons. A semi-analytic formula encapsulates the overall scaling with energy and scattering length, as well as resonant modifications by the presence of borromean N-body states near the threshold collision energy in the entrance channel. We then apply our model to the case of four-boson recombination into an Efimov trimer and a free atom.
We discuss collision of three identical particles and derive scattering selection rules from initial to final states of the particles. We use either laboratory-frame, hyperspherical, or Jacobian coordinates depending on which one is best suited to describe three different configurations of the particles: (1) three free particles, (2) a quasi-bound trimer, or (3) a dimer and a free particle. We summarize quantum numbers conserved during the collision as well as quantum numbers that are appropriate for a given configuration but may change during the scattering process. The total symmetry of the …
Precise spectral diagnostic modelling of H~{\sc i} and He~{\sc ii} recombination spectra can constrain theoretical models which describe many astrophysical environments. Simple analytic expressions are of interest for collisional $l$-changing rate coefficients that are used by large-scale population modelling codes. We review, clarify and improve-upon the modified Pengelly \& Seaton formulae of Guzmán \etal We show that the recent poor results for it shown by Vrinceanu \etal are due to their misinterpretation of its usage. We also detail efficient numerical algorithms which should enable the f…
We show that in the limit of large and positive atom--atom scattering length the properties of an atomic--molecular Bose--Einstein Condensate (amBEC) are determined by an universal energy density functional (EDF). We find that the optimal conditions for the formation of a stable amBEC are in the regime where there are no shallow trimers and the atom--dimer scattering length is negative and comparable in magnitude with the atom--atom scattering length. At temperatures lower than $T_c$ the chemical potentials for the atoms and molecules can be specified independently. Besides three--body recombi…
