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good agreement between the experimental results and quantum dynamics calculations based on the rigid rotor model using a PES reported by Diep and Johnson (DJ) [129]. Montero et al. [130] have investigated cold inelastic collisions of n-H$_{2}$ molecules in the ground vibrational state, using a 3:1 gas mixture of ortho and para hydrogen. They obtained good agreement between the experimental data and the theoretical calculations based on the DJ PES. 

Using a quantum formalism based on the rigid rotor model, Lee et al. [126] have recently presented a compar- ative analysis of cross sections for rotationally-inelastic collisions between H$_{2}$ molecules at low and ultra-low energies. The elastic cross sections for H$_{2}$( v = 0 , j = 0) + H$_{2}$( v ′ = 0 , j ′ = 0) collisions obtained in this study are presented in Fig. 23 for two different PESs. The limiting value of the elastic scattering cross section in the ultra-low energy regime is 1 . 91 × 10 $_{−}$13 cm 2 with the PES of Boothroyd, Martin, Keogh and Peterson (BMKP) [131] and 1 . 74 × 10 $_{−}$13 cm 2 with the DJ PES [129]. For low collision energies the dynamics is sensitive to higher-order anisotropic terms in the angular expansion of the interaction potential. A diatom - diatom scattering length of 5.88 ˚ A was obtained for the DJ PES and 6.16 ˚ A for the BMKP PES. Cross sections for the quenching of rotationally excited H$_{2}$ molecules in H$_{2}$( v = 0 , j = 2) + H$_{2}$( v ′ = 0 , j ′ = 0) and H$_{2}$( v = 0 , j = 2) + H$_{2}$( v ′ = 0 , j ′ = 2) collisions were presented at low and ultra-low energies. 

Quantum calculations of rotational relaxation of CO in cold and ultracold collisions with H$_{2}$ have recently been performed by Yang et al. [132, 133]. They reported quenching rate coefficients for j = 1 − 3 of the CO molecule in collisions with both ortho- and para-H$_{2}$ [132]. Due to the relatively deep van der Waals interaction potential for the H$_{2}$ − CO system the 

cross sections exhibit a number of narrow resonances for collision energies between 1 . 0 − 40 . 0 cm $^{$_{−}$1}$. The signatures of these resonances are present in the tem- perature dependence of the rate coefficient which shows broad oscillatory features in the temperature range of 10 $_{−}$2 − 50 K [132]. 

Bohn and co-workers have reported extensive calcu- lations of hyperfine transitions in ultracold molecule - molecule collisions. Avdeenkov and Bohn studied ultra- cold collisions between O$_{2}$ molecules [134]. They used a quantum mechanical formalism based on the rigid rotor model and included the electronic spin structure of the O$_{2}$ molecules. Couplings between the rotational angu- lar momentum and the electronic spin of the molecules lead to rotational fine structure. Avdeenkov and Bohn discussed the elastic and inelastic loss processes in $^{17}$O$_{2}$ + $^{17}$O$_{2}$ and $^{16}$O$_{2}$ + $^{16}$O$_{2}$ collisions. They found that for collision energies below 10 $_{−}$2 K, elastic collision cross sections are larger than inelastic spin-flipping transi- tions. Based on relative magnitudes of elastic and in- elastic spin-flipping cross sections they concluded that $^{17}$O$_{2}$ molecules would be good candidates for evaporative cooling. In contrast, for $^{16}$O$_{2}$ + $^{16}$O$_{2}$ collisions, inelastic processes are more efficient than elastic collisions so that $^{16}$O$_{2}$ molecules are prone to collisional trap loss. 

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Avdeenkov and Bohn also studied ultracold collisions between OH [135, 136] and OD radicals [137] in the pres- ence of an applied electric field. They showed that [137], elastic scattering is more efficient than inelastic processes for ultracold collisions between fermionic OD molecules, inhibiting state changing collisions. The energy depen- dence of elastic and inelastic cross sections for OH + OH and OD + OD collisions is illustrated in Fig. 24 for an applied electric field of ε =100 V/cm. While the elastic 

