On the capture cross-section for charge neutralization, recombination, photoassociation and other barrierless reactions

The collision energy dependence of cross-section for reactions where the reactants attract is discussed. Examples include charge recombination A⁺ + B^- → products, ion-molecule reactions and other curve crossing processes. The common characteristic of such processes is that on physical grounds there is a critical distance d where capture occurs. Special attention is given to the case where the critical separation is independent of energy and/or impact parameter. A modern example where this is the case is laser-induced association of atoms. The capture cross-section has the functional form σ = πd²(1 - V_g(d)/E_T) where for the collisions discussed the potential is attractive, V_g(d) < 0. Such a cross-section is a decreasing function of the collision energy E_T. The same functional form is also useful if the potential is repulsive, V_g(d) > 0. For this well-known case, the cross-section is an increasing function of the collision energy.