Time-dependent density-functional-theory studies of collisions involving He atoms: Extension of an adiabatic correlation-integral model

A recent model to describe electron correlations in time-dependent density-functional-theory (TDDFT) studies of antiproton-helium collisions is extended to deal with positively charged projectiles. The main complication is that a positively charged projectile can capture electrons in addition to ionizing them to the continuum. As a consequence, within the TDDFT framework one needs to consider three, instead of just one, correlation integrals (Ic's) when formally expressing the probabilities for the one- and two-electron processes in terms of the density. We discuss an extension of an adiabatic model for Ic to a two-centered system. Total cross sections for single ionization, double ionization, single capture, transfer ionization, and double capture are presented for both proton-helium and He²⁺-He collisions for impact energies in the approximate range 10--1000 keV/amu. One- and two-electron removal cross sections are also presented for the p-He system, with a comparison to updated antiproton-helium results. Our results, while mixed, demonstrate the relative importance of dynamic and functional correlations in a TDDFT description of collision processes.