Single Electron Capture in Collisions of Fast Ions with Molecular Hydrogen in the Impact Parameter Representation

A theoretical method for evaluating the single-electron capture (SEC) cross sections in collisions of fast ions with a ground-state H₂ molecule is presented. The scattering problem for ion-molecule collisions is formulated in the impact parameter representation using the relation between the quantum-mechanical amplitude and quasi-classical impact parameter one. The capture amplitudes and corresponding probabilities of capture to (nlm) states of an incident ion are derived within the framework of the Brinkman–Kramers approximation. The general expressions for the SEC probability amplitudes to n-states, summed over l and m quantum numbers, are deduced, from which the corresponding SEC probabilities can be then calculated using a procedure of multichannel normalization. The dependence of the differential cross sections, integrated over projectile impact parameters, on the molecular orientation for charge exchange in H⁺ + H₂ collisions is considered and compared with measurements and other calculations. Total SEC cross sections, integrated over the molecular orientations and summed over n-states for several bare and dressed ions, are calculated and compared with available experimental data and results of calculations by means of other theoretical methods.