-150 -100 -50 0 50 100 150  (¯) 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9 10 -8 R(T=0) (cm 3 •s -1 ) 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Mass of both H atoms 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 |  Re(E p )  |  (meV) 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 Kinetic energy (eV) 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 Cross section (10 -16 cm 2 ) 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 Cross section (10 -16 cm 2 ) FIG. 13: Cross sections for LiF formation (solid curve) and non-reactive scattering (dashed curve) in Li + HF( v, j = 0) collisions as functions of the incident kinetic energy: results for v = 0 (lower panel); results for v = 1 (upper panel). Re- produced with permission from Weck and Balakrishnan [84]. FIG. 12: Real part of the scattering length (upper panel), zero-temperature limiting values of the rate coefficient (mid- dle panel), and positions of quasibound states (lower panel) of the F · · · H 2 complex as functions of the mass of a pseudo hydrogen atom. Reproduced with permission from Bodo et al. [75]. refers to the process in which a rotationally or vibra- tionally excited van der Waals complex decays through chemical reaction rather than by rotational or vibrational predissociation. For reactions with energy barriers the chemical reaction pathway may involve tunneling. The reactions of Cl with H$_{2}$ and HD are dominated by tun- neling at low temperatures [81–83]. Compared to the F + H$_{2}$ and F + HD reactions, the energy barrier for the Cl + H$_{2}$ reaction is much larger and the reactivity at low energies is significantly suppressed. Nearly a decade ago, Skouteris et al. [81] showed that the van der Waals interaction potential between Cl and HD determines the reaction outcome, despite the fact that the depth of the van der Waals interaction potential for the Cl · · · HD sys- tem is less than one-tenth of the height of the reaction barrier. Quantum scattering calculations of the Cl + HD reaction on PESs without the van der Waals interac- tion potential predict nearly equal probabilities for HCl and DCl products [81]. However, if the potential surface includes the van der Waals interaction a strong prefer- ence for the DCl product occurs at thermal energies, in agreement with experimental results. The effect of these weakly bound states on the reactivity at cold and ultra- cold temperatures has recently been explored by Balakr- ishnan [82]. results for both Li + HF [84] and LiF + H [85] reactions with thermal and non-thermal vibrational excitation sug- gest that heavy-atom tunneling may play an important role in chemical reactions at cold and ultracold temper- atures. An experimental study [12] of an organic ring expansion reaction at 8 K has shown that the reaction occurs almost exclusively by carbon tunneling. The tun- neling contribution was found to be orders of magnitude greater than over the barrier contribution. In a recent work, Tscherbul and Krems [93] have explored the Li + HF and LiF + H reactions in the presence of an external electric field. They have shown that, for temperatures below 1 K, the reaction probability can be significantly influenced by electric fields. The cross sections for HCl and DCl formation and non- reactive rovibrational transitions in Cl + HD( v = 1 , j = 0) collisions for total angular momentum quantum num- ber J = 0 are shown in Fig. 14 as functions of the to- tal energy [82]. The sharp features in the cross sections correspond to Feshbach resonances arising from the de- cay of quasibound van der Waals complexes formed in the entrance channel of the reaction. The quasibound states can be identified by examining bound states of adiabatic potentials correlating with the v = 1 , j = 0 and v = 1 , j = 1 levels of the HD molecule. They are Van der Waals complexes formed during collisions can either undergo vibrational predissociation or vibrational prereaction leading to sharp features in the energy de- pendence of the cross sections. The term “prereaction” 2. Feshbach resonances in reactive scattering 12