16 predicts results in very close agreement with the experi- mental result of Wynar et al. [108]. Thus, the Langevin model appears to be valid for describing collisional prop- erties of these systems at µ K temperatures. The model also confirms that cold and ultracold collisions of alkali metal atoms and dimers are essentially characterized by the leading term in the long-range part of the interaction p otential. al. [94], who showed that in the Langevin regime the rate coefficients become independent of the vibrational level of the molecule. The third region is intermediate be- tween the Wigner and Langevin regimes, which typically corresponds to a quantum calculation with two or three partial waves. As shown in the lower panel of Fig. 17 the height of each J -resolved effective barrier depicted by vertical lines for J = 1 − 5 corresponds approximately to the maximum of each J -resolved quenching rate co- efficient. This indicates that the quenching process be- comes significant when the barrier height is energetically overcome. Whenever the elastic and quenching rate co- efficients have comparable values, the Langevin regime is reached, as shown in Fig. 17. Since the quenching prob- ability is almost equal to one and the elastic probability is almost equal to zero, elastic and quenching transition matrix elements are both equal to one and the cross sec- tions and rate coefficients for the two processes become similar. 0 100 200 300 400 500 600 T ( K) 0.1 1 k Lang  (10 -10  cm 3  s -1 ) Rb + Rb$_{2}$ Rb + Rb$_{2}$, Wynar et al. (exp, 2000) Cs + Cs$_{2}$ Cs + Cs$_{2}$, Staanum et al. (exp, 2006) Cs + Cs$_{2}$, Zahzam et al. (exp, 2006) Rb + RbCs Rb + RbCs, Hudson et al. (exp, 2008) Cs + RbCs Cs + RbCs, Hudson et al. (exp, 2008) RbCs + RbCs FIG. 18: Rate coefficients as functions of the temperature predicted by the Langevin model compared with experimen- tal data for different collisional processes involving Rb or Cs atoms. The curves correspond to the Langevin results and the symbols denote the experimental results. The above analysis shows that at energies above the onset of the Wigner regime the Langevin model can cor- rectly describe the dynamics for barrierless atom - dimer alkali-metal collisions because of the strong inelastic cou- plings. However, the classical model is not suitable for tunneling dominated reactions. Accurate quantum dy- namics calculations are computationally demanding for heavier systems such as Cs + Cs$_{2}$, Rb + Rb$_{2}$, Rb + RbCs or Cs + RbCs and the classical model may be used to qualitatively describe the dynamics of these sys- tems at energies above the s-wave regime. The tempera- ture dependence of the rate coefficients predicted by the Langevin model is given by the simple formula in atomic units: Potential energy surfaces are the key ingredients that enter in quantum dynamics calculations. While the two- body terms are generally well known and accurate, the three-body terms are more difficult to compute with high precision since they are non-additive and involve correla- tions between the three atoms. As a consequence, quan- tum dynamics calculations may suffer from the quality and degree of accuracy of the three-body terms. The sensitivity of the ultracold collision cross sections to the details of the PES has been investigated for atom - dimer alkali-metal systems by Qu´em´ener et al. [99] for Na + Na$_{2}$( v = 1 − 3 , j = 0) and by Cvitaˇs et al. [97] for Li + Li$_{2}$( v = 0 − 3 , j = 0). In these studies, a linear scal- ing factor λ has been included to tune the three-body interaction term in the PES and cross sections were cal- culated as a function of λ . Other studies have com- pared the dynamics with and without the three-body terms for Na + Na$_{2}$( v = 1 , j = 0) [98] and for Li + Li$_{2}$( v = 0 − 10 , j = 0) [96] collisions. 2. Role of PES in determining ultracold reactions k$_{Lang}$ ( T ) = π ( 8 k$_{B}$T πµ ) 1 / $^{2}$( 2 C$_{6}$ k$_{B}$T ) 1 / 3 Γ(2 / 3) where µ is the reduced mass of the atom - diatom colli- sional system and C$_{6}$ the dominant atom - diatom long range coefficient. In Fig. 18 we show the rate coefficients predicted by the Langevin model as functions of the tem- perature for different atom - diatom and diatom - di- atom collisions involving Rb or Cs atoms. For Rb − RbCs, Cs − RbCs, and RbCs − RbCs collisions we used the corre- sponding C$_{6}$ coefficients calculated by Hudson et al. [111]. In the absence of similar data for Cs + Cs$_{2}$ and Rb + Rb$_{2}$ collisions, we approximated the atom - dimer C$_{6}$ coeffi- cient by multiplying the corresponding atom - atom value by a factor of two. For Cs + Cs$_{2}$ collisions we used the C$_{6}$ coefficient for Cs − Cs interaction calculated by Amiot et al. [112] and for Rb + Rb$_{2}$ collisions we adopted the C$_{6}$ coefficient for Rb − Rb interaction reported by Derevianko et al. [113]. As shown in Fig. 18 the Langevin model pre- dicts rate coefficients within an order of magnitude of the experimental values for the different systems. The predicted results for the Cs + Cs$_{2}$, Rb + RbCs, and Cs + RbCs collisions agree with the corresponding experi- mental data of Refs. [106, 107, 111] within the reported error bars. For Rb + Rb$_{2}$ collisions the Langevin model The dependence of the total quenching cross sections on the three body term for Na + Na$_{2}$( v = 1 − 3 , j = 0) scattering [99] at a collision energy of 10 $_{−}$9 K is shown in Fig. 19. The contribution of each final vibrational level is also plotted. For the v = 1 vibrational level, the cross sections are very sensitive to the details of the three-body