A quantum-fluid density-functional theory (QF DFT) is proposed, yielding a time-dependent (TD) generalized nonlinear Schrödinger equation (GNLSE) as the equation of motion (EOM) for dealing with proton–helium-atom collisions from ‘‘start’’ to ‘‘finish.’’ The EOM contains the Weizsäcker term as the kinetic-energy functional, apart from local exchange and correlation functionals. The GNLSE is numerically solved in cylindrical polar coordinates by a leapfrog-type finite-difference algorithm. Various TD quantities such as difference density (DD), induced-dipole moment (IDM), dipole polarizability tensor component, reaction probability, etc., have been studied to obtain physical insights into the mechanism of the TD collision process. In particular, the DD and the oscillating IDM permit a natural partitioning of the p-He collision process into approach, encounter, and departure regimes. The TD DD profiles reveal that, as a result of the interaction, pσ densities mix substantially into the 1s density of the He atom. Critical comments are made on the usefulness of the QF DFT approach for understanding TD processes.

• Received 9 July 1990

DOI:https://doi.org/10.1103/PhysRevA.43.1248