molecules induced by structureless atoms occur through coupling to the rotationally excited N > 0 levels and that the corresponding rate coefficients are determined by the spin-rotation interaction with the transiently rotationally excited molecule. Table I provides a compilation of zero-temperature quenching rate coefficients for vibrational and rotational relaxation in a number of atom - diatom systems. system initial ( v, j ) k$_{T}$ =0 (cm $^{3}$s − $^{1}$) Ref. H + H 2 ( v = 1 , j = 0) 1.0 × 10 − 17 [28] $^{3}$He + H 2 ( v = 1 , j = 0) 3 × 10 − 17 [19] ( v = 10 , j = 0) 3.6 × 10 − 14 [19] $^{4}$He + CO ( v = 1 , j = 0) 6.5 × 10 − 21 [23] ( v = 1 , j = 1) 9.0 × 10 − 19 [23] $^{3}$He + CO ( v = 1 , j = 0) 1.3 × 10 − 19 [40] ( v = 2 , j = 0) 2.1 × 10 − 19 [40] $^{4}$He + CO ( v = 1 , j = 0) 5.3 × 10 − 21 [40] ( v = 2 , j = 0) 1.3 × 10 − 20 [40] $^{3}$He + CaH ( v = 0 , j = 1) 3.5 × 10 − 12 [49] ( v = 1 , j = 0) 2.6 × 10 − 17 [49] $^{3}$He + HF ( v = 1 , j = 0) 3.1 × 10 − 16 [40] ( v = 2 , j = 0) 2.6 × 10 − 15 [40] $^{4}$He + HF ( v = 1 , j = 0) 8.1 × 10 − 16 [40] ( v = 2 , j = 0) 6.5 × 10 − 15 [40] $^{3}$He + LiH ( v = 1 , j = 0) 9.0 × 10 − 14 [40] ( v = 2 , j = 0) 3.6 × 10 − 12 [40] $^{4}$He + LiH ( v = 1 , j = 0) 3.8 × 10 − 13 [40] ( v = 2 , j = 0) 1.5 × 10 − 11 [40] At energies above the onset of the s-wave regime, cross sections will be dominated by contributions from non- zero angular momentum partial waves. If the interac- tion potential includes an attractive part, the effective potentials for non-zero angular momentum partial waves may possess centrifugal barriers that introduce shape res- onances in the collision energy dependence of the cross section. This is illustrated in Fig.4 for the vibrational relaxation of CO( v = 1 , j = 0) in collisions with $^{4}$He atoms. The sharp features in the energy dependence of the cross section for energies between 0.1 and 10.0 cm $_{−}$1 arises from shape resonances supported by the van der Waals interaction potential between He and the CO molecule. As shown in Fig.5, when integrated over the ve- locity distribution of the colliding species the shape reso- nances lead to significant enhancement of the vibrational relaxation rate coefficient for temperatures between 0.1 and 10.0 K. Similar results have been found for vibra- tional relaxation of CO [24], O$_{2}$[25], and CaH [49] in collisions with $^{3}$He atoms. The sharp features in the en- ergy dependence of the vibrational relaxation cross sec- tions for the Ar + D$_{2}$ sytem shown in Fig.2 also arises from shape resonances supported by the Ar − D$_{2}$ van der Waals potential. The effect is generally more pronounced for systems composed of heavier diatomic molecules and interaction potentials with deep van der Waals wells for which the density of states will be much higher leading to rich resonance structures in the cross sections. Feshbach resonances occur in multichannel scattering in which an unbound (continuum) channel is coupled to a bound state of another channel. If the energy of the interacting system in the unbound channel lies close to that of the bound state and the coupling between the two channels is strong the cross section may change dramat- ically in the vicinity of the resonance. In the Feshbach resonance method for producing ultracold molecules, an external magnetic field is used to tune the energy of the bound pair to that of the the separated atoms. In atom - diatom systems, the bound state may correspond to a quasibound state of the atom - diatom van der Waals complex. Channel potentials corresponding to different initial vibrational and rotational levels of the diatom may induce Feshbach resonances. For the He − CO system Feshbach resonances were found to occur near channel thresholds corresponding to the j = 1 rotational level TABLE I: Zero-temperature inelastic rate coefficients for dif- ferent atom - molecule systems. FIG. 4: Cross section for the quenching of the v = 1 , j = 0 level of CO in collisions with $^{4}$He as a function of the incident kinetic energy. Reproduced with permission from Balakrish- nan et al. [23]. 6 2. Shape resonances in molecular collisions 3. Feshbach resonances in molecular collisions 10 −5 10 −3 10 −1 10 1 10 3 Energy (cm −1 ) 10 −9 10 −8 10 −7 10 −6 10 −5 Cross section (10 −16 cm 2 )