15 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 Collision energy (K) 10 -13 10 -12 10 -11 10 -10 Elastic rate coefficient (cm 3 .s -1 ) total J=[0-5] 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 Collision energy (K) 10 -11 10 -10 Quenching rate coefficient (cm 3 .s -1 ) total Langevin J=[0-5] FIG. 17: Elastic (upper panel) and quenching (lower panel) rate coefficients versus the collision energy for $^{39}$K + $^{39}$K 2 ( v = 1 , j = 0) scattering. The rate coefficient from a capture model is also shown for the quenching processes. Adapted with per- mission from Qu´ em´ ener et al. [100]. For heavy systems such as alkali-metal systems, the density of states is very large and the narrow energy spacing can lead to very strong couplings, especially in the vicinity of avoided crossings. The strong couplings will lead to efficient energy transfer between different quantum states. This may also explain the relatively weak dependence of the vibrational quenching rate coef- ficients on the initial vibrational state of the molecule in atom - dimer alkali-metal collisions. Fig. 17 provides a comparison between elastic and quenching rate coefficients for $^{39}$K + $^{39}$K$_{2}$ ( v = 1 , j = 0) [100] collisions at energies ranging from 10 $_{−}$9 K to 10 $_{−}$2 K. The results include contributions from the total angular momentum quantum numbers J = 0 − 5. For low vibrational states of the K$_{2}$ dimer, quenching pro- cesses are more efficient than elastic scattering at ultra- cold energies. For example, at a temperature of 10 $_{−}$9 K, the quenching rate coefficient is about 10 $_{−}$10 cm 3 s $_{−}$1 compared to 10 $_{−}$13 cm 3 s $_{−}$1 for elastic scattering. The quenching processes lead to collisional relaxation of the molecules to lower ro-vibrational states resulting in trap loss. Similar results have been obtained for Na + Na$_{2}$ [98, 99] and Li + Li$_{2}$ [94, 96, 97] collisions. The zero-energy quenching rate coefficients for these systems are found to be on the order of 10 $_{−}$11 − 10 $_{−}$10 cm 3 s $^{$_{−}$1}$. The quenching processes are more efficient than the elastic collisions at ultracold temperatures. Thus, quenching of vibrationally excited alkali-metal dimers in collisions with alkali-metal atoms occurs with significant rates at ultracold temperatures. The typical magnitude of these rate coefficients from the scattering calculations is in reasonable agreement with experimental results. In a recent experiment, Staanum et al. [106] reported a value of 9 . 8 × 10 $_{−}$11 cm 3 s $_{−}$1 for the relaxation of low-lying vibrational levels of Cs$_{2}$ in collisions with Cs atoms at a temperature of 60 × 10 $_{−}$6 K. In a separate experiment, Zahzam et al. [107] determined a quenching rate coefficient of 2 . 6 × 10 $_{−}$11 cm 3 s $_{−}$1 for the same sys- tem at a temperature of 40 × 10 $_{−}$6 K. Wynar et al. [108] estimated inelastic rate coefficients of 8 × 10 $_{−}$11 cm 3 s $_{−}$1 for Rb + Rb$_{2}$ collisions. Mukaiyama et al. [109] reported an inelastic rate coefficient of 5 . 5 × 10 $_{−}$11 cm 3 s $_{−}$1 for collisions of Na atoms with Na$_{2}$ molecules created by the Feshbach resonance method while Syassen et al. [110] obtained a value of 2 × 10 $_{−}$10 cm 3 s $_{−}$1 for collisions of Rb atoms with Rb$_{2}$ molecules. model is based on the assumption that if the total energy of the system can overcome the effective barrier, then the elastic probability is zero and the quenching probabil- ity is one. Otherwise, the elastic probability is one and the quenching probability is zero. Classically, the barrier prevents the atom and the molecule from accessing the region of strong coupling with the other channels. Results obtained using the Langevin model for the K + K$_{2}$ system are shown in Fig. 17 along with the quan- tum results. As Fig. 17 illustrates, three different regions can be distinguished for the K + K$_{2}$ system. The first region, for collision energies below 10 $_{−}$6 K, corresponds to the Wigner regime where the threshold laws apply. In this regime, the quenching rate coefficient tends to a constant while the elastic component approaches zero as the square root of the collision energy. A quantum de- scription is required and classical models cannot describe the dynamics in this regime. The second region, above a collision energy of 10 $_{−}$3 K, corresponds to the Langevin regime. Here, the difference between the full quantum calculation and the classical model is within 10 %. Simi- lar results have been found for $^{7}$Li + $^{7}$Li$_{2}$ ( v = 1 , 2 , j = 0) and $^{6}$Li + $^{6}$Li$_{2}$ ( v = 1 , 2 , j = 1) collisions by Cvitaˇs et At large atom - diatom separations, R , the interaction potential can be approximated by an effective potential, composed of a repulsive centrifugal term and the long range interaction potential. For alkali-metal trimer sys- tems, the atom - diatom long range potential is a van der Waals interaction potential and behaves as - C$_{6}$ /R $^{6}$. The classical capture model (also known as the Langevin model) has been shown to work quite well for these sys- tems [100] at certain energy regimes. The Langevin