A source of errors in cross sections of curve-crossing processes

Total inelastic cross sections for atomic collisions are usually obtained by computing the complex phaseshifts of the incident wavefunction often using perturbation techniques. Such calculations are generally based on a theoretical formalism in which a local complex potential, V(R)-i 1 / 2 Gamma (R), is employed to describe the entrance channel. However, the assumption that the imaginary component is local breaks down when there are only a few final states energetically open. The characteristics of the effects associated with this breakdown are discussed through a numerical study of the associative detachment process H+H - ( 1 Sigma g + ) to H 2 ( 2 Sigma u + )+e - at incident energies of 0.0129, 0.129 and 0.646 eV. The cross sections to individual vibrational-rotational levels of H 2 are also reported. It is shown that the breakdown in the expression often used for a local complex potential can produce substantial errors in computed cross sections. Methods of detecting and analysing the divergence of calculated cross sections from true ones are presented, along with means of estimating actual values within uncertainty brackets.