Three-Body Recombination of ${}^6\mathrm{Li}$ Atoms 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 ${}^6\mathrm{Li}$ atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.

Figure 1

The coefficients $C$ scaled by $(a_{23}/a{)}^{-2}$ (upper curve) and $D$ (lower curve) in Eq. (7) as functions of $a_{23}/a$ for the case of two equal negative scattering lengths $a$ and a third negative scattering length $a_{23}$.

Figure 2

The scattering lengths for the three lowest hyperfine states of ${}^6\mathrm{Li}$ as functions of the magnetic field $B$ [16]. The vertical scale changes by a factor of 10 at $B=600\mathrm{G}$. The two vertical dotted lines mark the boundaries of a region in which $|a_{12}|>2{\ell }_{\mathrm{vdW}}$. The three vertical dashed lines mark the positions of the Feshbach resonances.

Figure 3

The three-body recombination rate constant $K_3$ as a function of the magnetic field $B$. The two vertical dotted lines mark the boundaries of the region in which $|a_{12}|>2{\ell }_{\mathrm{vdW}}$. The solid squares and dots are data points from Refs. 6, 7, respectively. The curve is a 2-parameter fit to the shape of the data from Ref. 6.

Figure 4

The three-body recombination rate constant $K_3$ as a function of the magnetic field $B$. The three vertical dashed lines mark the positions of the Feshbach resonances. The solid dots are data points from Ref. 7. The curve is a 2-parameter fit to the last two data points.