Low-energy limit for tunnelling subject to an Eckart potential barrier

For two-body s-wave collisions subject to tunnelling though an Eckart potential barrier, cross-sections and rate coefficients in the low-energy regime can be evaluated in analytic form. These provide criteria for approach to the Wigner limit and a generic plot applicable to ultracold collisions (<1 mK). The Eckart barrier shape is found to fit fairly well accurate potential curves available for F(P) + F(P) and He(1S) + He*( S). Also discussed are tunnelling-dominated ultracold chemical reactions, exemplified by F + H. The very slow approach of the reactants allows averaging over rovibrational motions, so the effective adiabatic ('dressed') potential surface differs substantially from the Born-Oppenheimer ('bare') surface obtained from electronic structure calculations. The dressed barrier is more than two-fold lower and also thinner. For it the Eckart model gives an ultracold rate coefficient for forming HF in its v' = 2, j' = 0 rovibrational state (6.5 × 10 cm /s) that is about 200-fold higher than for the bare barrier and of the same magnitude found from a full-scale 3-D quantum scattering calculation. © 2010 Taylor & Francis.