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where the zero-temperature vibrational and rotational transition rate coefficients for different initial vibrational levels of the H$_{2}$ molecule are plotted as functions of the initial rotational level. For initial rotational levels greater than 12 the QR transition becomes the dominant energy transfer mechanism compared to pure rotational quench- ing. The gap at j = 22 occurs because the Δ j = − 2Δ v transition is energetically not accessible for this initial state at zero temperature. Forrey et al. [21] found that the QR process is even more dominant at low temper- atures than at thermal energies. Remarkably, classical trajectory calculations [21] were successful in correctly predicting the correlation between Δ j and Δ v at ultra- cold temperatures even though the changes in v and j were fractional. Extensive studies of QR energy transfer in cold and ultracold temperatures have been reported by Forrey et al. [56–59]. Ruiz and Heller [60] have recently published a review paper providing a detailed analysis of QR phenomenon using semi-classical techniques. McCaf- fery and coworkers [61–63] have also reported a number of quasi-classical trajectory calculations of the QR process in thermal energy collisions and successfully interpreted a large body of experimental data based on the QR phe- nomenon and simple parametric models. 

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Dynamics of ionic systems are different from collisions of neutral species. The short-range part of the interaction potential for ionic systems is usually more anisotropic and the long-range part has an attractive component 

## C. Atom - molecular ion collisions 

which is determined by the polarizability of the atom and it vanishes as 1 /R 4 where R is the atom - molecule center- of-mass distance [64]. Due to the strong polarizability term, the interaction potential for ionic systems extends to longer range compared to neutral atom - molecule sys- tems. Therefore, it is important to understand the effect of both the short and long range part of the interaction potential on the scattering dynamics. For this purpose, several studies have focused on ultracold collisions be- tween molecular ions and neutral atoms as well as neutral molecules and atomic ions. 

Bodo et al. [64] investigated rotational quenching in Ne + 2 + Ne and He + 2 + He collisions at ultra-low energies. They found that the Wigner regime begins at a collision energy of 10 $_{−}$4 cm $_{−}$1 for the He system and 10 $_{−}$6 cm $_{−}$1 for the Ne system. In general, the s-wave Wigner regime was found to occur at lower energies for ionic systems compared to neutral species. For example, in He + H$_{2}$ [19] and He + O$_{2}$ [25] collisions the Wigner regime begins at collision energies of about 10 $_{−}$2 cm $^{$_{−}$1}$. The differences are attributed to the long range of the ion - neutral interaction potential which enhances contributions from higher partial waves. The differences between the He and Ne systems can be attributed to the mass difference and to the strength of the long range interaction potentials. For the heavier Ne system the long range part is more attractive, which increases the contribution of higher-order partial waves at ultra-low energies. The magnitude of the zero-energy rate coeffi- cients for rotational quenching in these molecular ions is on the order of 10 $_{−}$9 cm 3 s $^{$_{−}$1}$, which is considerably larger than for collisions involving neutral species. 

Stoecklin et al. [65] have performed a comparative study of collisions of N + 2 ( v = 1 , j = 0) molecular ions with neutral $^{3}$He or $^{4}$He atoms, and the scattering of neutral N$_{2}$( v = 1 , j = 0) molecules in collisions with $^{3}$He or $^{4}$He atoms. The vibrational quenching cross sections for these systems are presented in Fig. 8. While the behavior of the quenching cross sections of neutral N$_{2}$ molecules with $^{3}$He and $^{4}$He atoms was found to be similar, they observed a striking difference between the quenching cross sections of N + 2 in collisions with $^{3}$He and $^{4}$He atoms. In particular, the resonance positions in the quenching cross sections were significantly shifted and the number of resonances was different. The N + 2 + $^{3}$He system has a shape resonance at a collision energy of 10 $_{−}$2 cm $_{−}$1 which is absent for the N + 2 + $^{4}$He system. Furthermore, the zero-energy quenching rate coefficient is an order of magnitude larger for collisions of N + 2 ( v = 1 , j = 0) with $^{3}$He than with $^{4}$He, whereas it is comparable for collisions of N$_{2}$( v = 1 , j = 0) with both $^{3}$He and $^{4}$He. The differences may be due to a virtual state in the N + 2 ( v = 1 , j = 0) + $^{3}$He collision system. More recently, Guillon et al. [66] studied the effect of spin-rotation interaction on vibrational and rotational quenching for the He − N + 2 system. They found that the vibrational quenching is not modified by 

