0 0.0002 0.0004 0.0006 0.0008 0.001 Collision energy (eV) 0 0.005 0.01 0.015 0.02 Cumulative reaction probabilities H$_{2}$ D$_{2}$ (x10) 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 Collision energy (eV) 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 Reaction cross section (Å 2 ) 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 Kinetic energy (eV) 10 −4 10 −3 10 −2 10 −1 10 0 10 1 10 2 Cross section (10 −16  cm 2 ) 11 FIG. 10: Comparison of J = 0 cross sections for F + HD( v = 0 , j = 0) → HF + D (solid curve), F + HD( v = 0 , j = 0) → DF + H (short-dashed curve) and F + H 2 ( v = 0 , j = 0) → HF + H (long-dashed curve) reactions as functions of the incident kinetic energy. Reproduced with permission from Balakrishnan and Dalgarno [74]. FIG. 11: Comparison of the J = 0 cumulative reaction prob- abilities (upper panel) and cross sections (lower sub-panel) of F + H 2 and F + D 2 reactions as functions of the incident kinetic energy. Reproduced with permission from Bodo et al. [75]. of Fig. 11). This feature was attributed to the presence of a virtual state. The enhancement of the limiting value of the rate coefficient for the F + H$_{2}$ reaction was also as- cribed to the virtual state. Evidence for the virtual state is the presence of a Ramsauer–Townsend minimum in the elastic cross section at an energy of about 3 × 10 $_{−}$5 eV and a negative value of the real part of the scattering length for the F + H$_{2}$ reaction [75]. erted by the HF molecule, the van der Waals interaction potential of the LiHF system is deeper compared to the F + H$_{2}$ system. The Li · · · HF van der Waals potential well is about 0.24 eV (1936.0 cm $^{$_{−}$1}$) and the H · · · LiF potential well is about 0.07 eV (565.0 cm $^{$_{−}$1}$). Quantum scattering calculations for Li + HF and LiF + H reac- tions by Weck and Balakrishnan [84, 85] with the PES of Aguado et al. [92] have shown that for incident energies below 10 $_{−}$3 eV the reaction cross section exhibits a large number of resonances. The energy dependence of the J = 0 cross section for Li + HF( v = 0 , j = 0) collisions is shown in Fig. 13. Detailed bound state calculations of the LiHF van der Waals complexes revealed that for the Li + HF( v = 0 , j = 0) reaction the resonances correspond to the decay of Li · · · HF( v = 0 , j = 1 − 4) van der Waals complexes. Calculations with vibrationally excited HF molecules showed that the reaction becomes about 600 times more efficient in the Wigner regime when HF is excited to the v = 1 vibrational level. As seen in Fig. 13, a unique feature of the Li + HF( v = 0 , j = 0) reac- tion is the presence of a strong peak at 5 . 0 × 10 $_{−}$4 eV at which the reaction cross section is about six orders of magnitude larger than the background cross section. The Another example of a tunneling dominated reaction is the Li + HF → LiF + H reaction. At cold and ultracold temperatures the reaction occurs by tunneling of the rel- atively heavy fluorine atom. The LiH + F channel is energetically not accessible at low energies and tunnel- ing of the H atom is not involved in this reaction at low temperatures. Due to strong electric dipole forces ex- To explore how isotope substitution modifies reac- tivity at low temperatures Bodo et al. [75] artificially varied the mass of the hydrogen atoms in the calculation for the F + H$_{2}$ reaction from 0.5 to 1.5 amu. As illustrated in Fig. 12, for an H atom mass of 1.12 amu the virtual state induces a zero energy resonance at which the real part of the scattering length diverged to infinity. For the same value of the H atom mass, the zero-temperature rate coefficient of the reaction attains a value of 1 . 0 × 10 $_{−}$9 cm 3 s $_{−}$1 which is about three orders of magnitude larger than that of the F + H$_{2}$ reaction in the Wigner limit. The variation of the scattering length of the F + H$_{2}$ system as a function of the mass of the pseudo-hydrogen atom is similar to the variation of scattering length as a function of the magnetic field in the vicinity of a Feshbach resonance.