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The recombination rate for three identical bosons has been calculated to test the limits of its universal behavior. It has been obtained for several different collision energies and scattering lengths (a) up to 10^5 a.u., giving rates that vary over 15 orders of magnitude. We find that universal behavior is limited to the threshold region characterized by E lesssim hbar^2/(2mu_{12}a^2), where E is the total energy and mu_{12} is the two-body reduced mass. The analytically predicted infinite series of resonance peaks and interference minima is truncated to no more than three of each for typical experimental parameters.Comment: 4 pages, 3 figure

The 4 He 3 system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term, to calculate all low-energy properties of the triatomic 4 He system. The bound state energies of the 4 He trimer are computed as well as the 4 He+ 4 He 2 elastic scattering cross sections, the three-body recombination and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4 He and one 3 He atoms, and compute the spectrum of the isotopic trimer 4 He 2 3 He, the 3 He+ 4 He 2 elastic scattering cross sections, the rates for three-body recombination and the collision induced dissociation rate at finite temperatures.The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems.

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Three-body recombination of identical, spin-polarized fermionic atoms in the ultracold limit is investigated. The mechanisms for recombination are described in terms of the "scattering volume" Vp in the framework of the adiabatic hyperspherical representation. We have calculated numerically the recombination rate K3 as a function of Vp and have found that K3 scales as |Vp| 8/3 for small |Vp|. A comparison with experimental data is also presented.PACS numbers: 34.10.+x,03.75.Fi Recently, the quantum degenerate regime was attained in ultracold gases of fermionic atoms such as 40 K [1] and 6 Li [2,3]. Part of the motivation for these experiments is to observe a pairing of fermions, leading to a superfluid state. One important factor limiting the achievable density in these degenerate Fermi gases (DFG's) of trapped atoms is the loss of atoms through three-body recombination. Such losses occur when three atoms scatter to form a molecular bound state and a third atom -K + K + K → K 2 + K, for instance. The kinetic energy of the final state particles causes them to escape from the trapping potential.While ultracold three-body recombination of identical, spin-polarized bosons has been theoretically studied because of its importance for Bose-Einstein condensates, recombination of identical fermions has not yet been considered. For bosons, Fedichev et al. [4] predicted that the recombination rate K 3 grows with the two-body s-wave scattering length a s , namely K 3 ∝ a 4 s , for a s > 0. This scaling was later confirmed by Nielsen and Macek [5] who also pointed out that it should hold for negative a s . The a 4 s scaling law for both signs of a s was indeed obtained by Esry et al. [6], Bedaque et al. [7], and Braaten and Hammer [8].In the case of fermions, however, the Pauli exclusion principle prohibits s-wave scattering of atoms in identical spin states, thus leaving only p-wave collisions. The relevant low-energy scattering parameter in this case is the two-body p-wave "scattering volume" defined aswhere δ p (k) is the p-wave scattering phase shift and k is the wave number. The scattering volume V p is related to the p-wave scattering length a p (see, for instance, Ref.[9]) by V p = a 3 p . We choose V p , rather than a p , as the parameter to characterize the three-body recombination of fermions since an artificial nonanalyticity is introduced into a p when taking the cube root of the quantity in the right-hand side of Eq. (1).Even though recombination of identical fermions is suppressed at ultracold temperatures by the Pauli principle, it does not vanish. In fact, it has been shown that the rate is proportional to E 2 at low collision energies [12]. While this rate remains negligible under typical experimental conditions, it can become substantial near a Feshbach resonance. The E 2 threshold law no longer applies, and the recombination rate tends to the limit imposed by unitarity -often comparable to or larger than the rates for boson systems. Feshbach resonances are, of course, extremely useful tools for the expe...