5 strongly on the collision partner. They reported rate coefficients in the range 10 $_{−}$21 − 10 $_{−}$19 cm 3 s $_{−}$1 for CO, 10 $^{$_{−}$16}$− 10 $_{−}$15 cm 3 s $_{−}$1 for HF, and 10 $^{$_{−}$14}$− 10 $_{−}$11 cm 3 s $_{−}$1 for LiH. The differences were attributed to the features of the intermolecular forces between the diatomic molecules and the He atoms. The interaction potential of the He − CO system is almost isotropic and is characterized by small vibrational couplings elements. The He − HF system is more anisotropic and the couplings between vibrational states are more significant. The interaction potential of the He − LiH system is very anisotropic and it exhibits strong vibrational couplings. tational relaxation of CO in $^{4}$He − CO collisions. The dy- namics of the He − CO system was found to exhibit signif- icantly different features at low temperatures compared to the He − H$_{2}$ system. Quantum scattering calculations of $^{4}$He and $^{3}$He collisions with the CO molecule revealed that the larger reduced mass and the deeper van der Waals interaction potential of the He − CO system give rise to a number of shape resonances in the energy de- pendence of vibrational relaxation cross sections [23, 24]. The effect of shape resonances on low temperature vi- brational relaxation rate coefficients will be discussed in the next subsection. The computed values of vibrational relaxation rate coefficients for both $^{3}$He and $^{4}$He colli- sions with CO( v = 1) have been found to be in good agreement with experimental data of Reid et al. [34] in the temperature range 35 − 100 K. Calculations of vibra- tional relaxation rate coefficients for the He − CO system in the temperature range 35 − 1500 K have also been re- ported by Krems [35]. He has shown that inclusion of the centrifugal distortion of the vibrational wavefunction enhances the relaxation process, and that the quenching rate coefficients are sensitive to high-order anisotropic terms in the angular expansion of the interaction poten- tial [36]. Bodo, Gianturco and Dalgarno [37] have extended the work of Balakrishnan et al. [23] to study the vibrational relaxation of excited CO( v = 2 , j = 0 , 1) molecules in collision with $^{4}$He atoms at ultra-low energies. They found that vibrational quenching of CO( v = 2 , j = 0 , 1) in collisions with $^{4}$He is dominated by the v = 2 → v = 1 transition. The cross sections for the v = 2 → v = 0 transition were found to be about four orders of mag- nitude smaller than the single quantum transitions for both j = 0 and j = 1 initial rotational levels. There is considerable ongoing experimental interest in cooling and trapping NH [41, 42] and OH [43, 44] molecules using the buffer gas cooling and Stark decel- eration methods described in the chapters by Doyle and by Meijer. Krems et al. [45] and Cybulski et al. [46] reported cross sections and rate coefficients for elastic scattering and Zeeman relaxation in $^{3}$He − NH collisions from ultralow energies to 10 cm $^{$_{−}$1}$. The calculations were performed using the rigid rotor approximation and an accurate He − NH PES. It was demonstrated that the elastic scattering of NH molecules with He atoms in weak magnetic fields is at least five orders of magnitude faster than the Zeeman relaxation, which suggests that the NH molecule is a good candidate for buffer-gas cooling. In a related study Gonz´ alez–S´ anchez et al. [47] examined rotational relaxation and spin-flipping in collisions of OH with He atoms at ultralow energies. They found that the rotational relaxation processes dominate the elastic process as the collision energy is decreased to zero. Ultracold vibrational relaxation of a number of other molecules in collisions with He atoms has been reported by a number of other investigators in recent years. Stoecklin, Voronin, and Rayez [38] reported the vibra- tional relaxation of F$_{2}$ in collisions with $^{3}$He atoms. In this study, they constructed the PES of He − F$_{2}$ us- ing ab initio points obtained by high-level molecular electronic-structure calculations, and reported the cross sections for elastic scattering and inelastic relaxation of F$_{2}$( v = 0 , 1 , j = 0) for collision energies in the range 10 $_{−}$6 − 2000 cm $^{$_{−}$1}$. A similar study has been reported by the same authors for the $^{3}$He + HF( v = 0 , 1 , j = 0 , 1) system [39]. The vibrational quenching cross sections were found to be very small compared to pure rota- tional quenching, in agreement with the results for the He − CO system. This is due to the weak dependence of the He − HF PES on the HF internuclear distance and the strong anisotropy of the interaction potential. While theoretical prediction of rate coefficients for vibrational and rotational relaxation in a number of atom - diatom systems has been made, comparable experimental results are not available for majority of these systems. The first measurements of vibrational relaxation of molecules at temperatures below 1 K were reported by Weinstein et al. [48]. In their study, CaH molecules slowed down by elastic collisions with $^{3}$He buffer gas atoms were trapped in an inhomogeneous magnetic field. An upper bound of the rate coefficients for spin-flipping transitions in CaH as well as vibrational relaxation of CaH molecules in the v = 1 vibrational level in collisions with $^{3}$He atoms were estimated at a temperature of about 500 mK. Balakrishnan et al. [49] presented a theoretical analysis of the vibra- tional relaxation of CaH in collisions with $^{3}$He atoms based on quantum close-coupling calculations and an ab initio PES for the He − CaH system developed by Groenenboom and Balakrishnan [50]. In a related study, Krems et al. [51] reported cross sections for spin-flipping transitions in CaH induced by collisions with $^{3}$He and obtained results in close agreement with the experimentally derived values of Weinstein et al [48]. Krems et al. demonstrated that at low energies, spin- flipping transitions in the N = 0 rotational level of $^{2}$Σ Bodo and Gianturco [40] presented a comparative study of vibrational relaxation of CO( v = 1 , 2 , j = 0), HF( v = 1 , 2 , j = 0) and LiH( v = 1 , 2 , j = 0) in colli- sions with $^{3}$He and $^{4}$He atoms in the Wigner regime. The quenching rate coefficients were found to depend