19 increased the density of states of the triatomic system, they found no significant dependence on the vibrational states of the molecule. However, for v = 10, they ob- tained the same results with and without the three-body term. The three-body term thus appears to be less signif- icant for collisions of molecules in high vibrational levels. Since the three-body term vanishes at large separations it is only important in the short-range interaction region while high vibrational states involve spatially extended molecules and sample the long range part of the interac- tion potential. Therefore, three-body terms, which are the most difficult interaction energy terms to compute numerically for triatomic systems, may be neglected to a first approximation in dynamics of highly vibrationally excited molecules. In the experiments, rate coefficients have been mea- sured for temperatures of 40 × 10 $_{−}$6 K [107] and 60 × 10 $_{−}$6 K [106] for Cs + Cs$_{2}$ while the theoretical rate co- efficients for Li + Li$_{2}$ were reported for a temperature of 10 $_{−}$9 K which corresponds to the Wigner threshold regime. Thus, it is likely that the experimental mea- surements did not probe the limiting values of the rate coefficients in the Wigner regime. Reactive collisions involving heteronuclear molecules are currently of great interest. A major goal of recent ex- periments has been to produce heteronuclear alkali-metal dimers in their electronic ground state. Examples include RbCs [111, 118, 119], NaCs [120, 121], KRb [122, 123], LiCs [124], and mixed isotopes $^{6}$Li$^{7}$Li [125]. Quan- tum dynamics calculations for heteronuclear systems are more difficult. They are more interesting from a chemistry perspective because the reactive channels in collisions of heteronuclear molecules can be distinguished from inelastic channels. Cvitaˇs et al. [95, 97] have explored the quantum dy- namics of $^{7}$Li + $^{6}$Li$^{7}$Li( v = 0 , j = 0), $^{7}$Li + $^{6}$Li$_{2}$ ( v = 0 , j = 1), $^{6}$Li + $^{7}$Li$_{2}$ ( v = 0 , j = 0), and $^{6}$Li + $^{6}$Li$^{7}$Li( v = 0 , j = 0) collisions. The J = 0 cross sections for elas- tic scattering and chemical reactions in collisions of $^{7}$Li with $^{6}$Li$^{7}$Li( v = 0 , j = 0) are presented in the upper panel in Fig. 22 for a wide range of collision energies. The cross sections are believed to be converged for en- ergies up to 10 $_{−}$4 K. The reactive process which leads to $^{6}$Li + $^{7}$Li$_{2}$ ( v = 0 , j = 0) dominates over the elastic scattering at ultralow energies. However, the reactive process is less efficient than the vibrational relaxation process in homonuclear alkali systems discussed above. For instance, at a collision energy of 10 $_{−}$9 K, the ratio of the cross sections for reactive and elastic collisions is about two orders of magnitude for the heteronuclear sys- tem presented in Fig. 22 whereas it is about three orders of magnitude for homonuclear systems. Cvitaˇs et al. at- These results provide important implications for the experiments on the production of $^{6}$Li$^{7}$Li in an ultracold mixture of $^{6}$Li and $^{7}$Li atoms. Cvitaˇs et al. proposed to remove quickly the $^{7}$Li atomic gas after the formation of the $^{6}$Li$^{7}$Li molecules in their ground state to prevent The J = 1 elastic and reactive cross sections for $^{7}$Li + $^{6}$Li$_{2}$ ( v = 0 , j = 1) collisions are presented in the lower panel of Fig. 22. The reactive process leading to the formation of $^{6}$Li$^{7}$Li molecules is slightly more efficient than elastic scattering in the Wigner regime. The other possible collision processes are $^{6}$Li + $^{6}$Li$^{7}$Li( v = 0 , j = 0) and $^{6}$Li + $^{7}$Li$_{2}$ ( v = 0 , j = 0). However, only elastic scattering occurs in these systems at ultralow collisions energies. tributed the smaller ratio to the presence of only one open channel in the heteronuclear reaction. FIG. 22: Elastic and reactive s-wave cross sections for $^{7}$Li + $^{6}$Li$^{7}$Li( v = 0 , j = 0) (upper panel) and $^{7}$Li + $^{6}$Li 2 ( v = 0 , j = 1) (lower panel). Reproduced with permission from Cvitaˇs et al. [95]. 4. Reactions of heteronuclear and isotopically substituted alkali-metal dimer systems 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 Collision energy (K) 10 −18 10 −17 10 −16 10 −15 10 −14 10 −13 10 −12 10 −11 10 −10 Cross section (cm 2 ) elastic: v$_{f}$=0, n$_{f}$=0 inelastic: v$_{f}$=0, n$_{f}$=1 reactive: v$_{f}$=0, n$_{f}$=0 reactive: v$_{f}$=0, n$_{f}$=2 0 0.2 0.4 0.6 0.8 1 10 −17 10 −16 10 −15 10 −14 10 −13 10 −12 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 E / K 10 −16 10 −15 10 −14 10 −13 10 −12 10 −11 10 −10 10 −9 10 −8  / cm 2 elastic: v$_{f}$=0, j$_{f}$=1 reactive: v$_{f}$=0, j$_{f}$=0 reactive: v$_{f}$=0, j$_{f}$=1 reactive: v$_{f}$=0, j$_{f}$=2 reactive: v$_{f}$=0 (total)