Radial-decoupling excitation mechanism in slow atomic collisions studied using zero-range model potentials

One-dimensional zero-range model potentials are employed to investigate the recently proposed radial-decoupling excitation mechanism in ion-atom collisions. The expression for the total (i.e. excitation plus ionization) radial-decoupling probability, obtained in the adiabatic limit, agrees with the result of our earlier, tentative approach (Pieksma and Ovchinnikov 1994 J. Phys. B: At. Mol. Opt. Phys. 27 4573) to second order in the collision velocity v. In fact, at low collision energies the cross section just scales with . This is in accordance with the adiabatic theorem as formulated by Born and Fock (1928 Z. Phys. 51 165), which also implies a power law for the cross section as the collision velocity becomes sufficiently low. The dependence is a purely quantal effect, and it is argued that it represents the correct low-energy cross section behaviour, even though it seems to contradict the exponential law that follows from the conventional theory of adiabatic transitions.