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the destructive reactive processes. But keeping the $^{6}$Li atomic gas is recommended for sympathetic cooling of the $^{6}$Li$^{7}$Li molecules since only elastic collisions are possible. Removing the $^{6}$Li atoms will leave the fermionic heteronuclear $^{6}$Li$^{7}$Li molecules in the trap. In the absence of $^{6}$Li atoms, evaporative cooling by collisions between fermionic $^{6}$Li$^{7}$Li molecules will not be effective since s-wave collisions of identical fermionic dimers will be suppressed due to the Pauli exclusion principle. 

Table IV provides a compilation of zero-temperature quenching rate coefficients for different alkali-metal trimer systems. 

## IV. INELASTIC MOLECULE - MOLECULE COLLISIONS 

Many of the studies of cold and ultracold molecules have focused on reactive and non-reactive scattering in atom - molecule collisions. At high densities of trapped molecules, molecule - molecule collisions need to be con- sidered. The presence of rotational and vibrational de- grees of freedom in both collision partners make molecule - molecule systems especially interesting. However, quan- tum dynamics calculations of molecule - molecule colli- sions are significantly more challenging. Most dynamical calculations of molecule - molecule scattering have relied on the rigid rotor approximation and some recent studies have adopted the coupled-states approximation. Calcula- tions performed at high collision energies have employed more approximate methods based on semi-classical tech- niques. Here, we present a brief account of recent dy- namical calculations for the H$_{2}$ + H$_{2}$ system and discuss some ongoing work on full-dimensional quantum calcu- lations of ro-vibrational transitions in H$_{2}$ − H$_{2}$ collisions. A brief discussion of hyperfine transitions in molecule - molecule systems is also provided for the illustrative ex- amples of the O$_{2}$ + O$_{2}$ and OH + OH / OD + OD systems. 

## A. Molecules in the ground vibrational state 

The H$_{2}$ + H$_{2}$ system is the simplest neutral tetra- atomic system and it serves as a prototype for describing collisions between diatomic molecules. Though there have been a number of experimental and theoretical studies over the past several years on the H$_{2}$ + H$_{2}$ system (see Ref. [126] and references therein), only a few studies have explored the collision dynamics in the cold and ultracold regime. 

Forrey [127] presented a study of rotational tran- sitions in H$_{2}$( v = 0 , j = 2) + H$_{2}$( v ′ = 0 , j ′ = 2) collisions at cold and ultracold collision energies using a rigid rotor model. He calculated the real and imagi- 

<img src='content_image/379144.jpg'>

nary components of the complex scattering length for H$_{2}$( v = 0 , j = 2 , 4 , 6 , 8) + H$_{2}$( v ′ = 0 , j ′ = j ) collisions and showed that the imaginary parts decrease with increasing j, j $^{′}$. The imaginary parts of the scattering lengths are found to be small compared to the real parts, leading to small inelastic cross sections. Mat´ e et al. [128] reported an experimental study of the rate coefficient for the H$_{2}$( v = 0 , j = 0) + H$_{2}$( v ′ = 0 , j ′ = 0) → H$_{2}$( v$_{f}$ = 0 , j$_{f}$ = 0) + H$_{2}$( v ′ f = 0 , j ′ f = 2) transition at temperatures between 2 K and 110 K. They found 

