Density-functional and hydrodynamical approach to ion-atom collisions through a new generalized nonlinear Schrödinger equation

This paper proposes a quantum-fluid density-functional theory (an interlinking of quantum-fluid dynamics and density-functional theory) for dealing with molecular collisions, in order to incorporate both time dependence and excited states. Using a new kinetic energy density functional for ion-atom collisions, we have derived a single-particle time-dependent single density equation for many-electron systems. The equation is a new generalized nonlinear Schr\"odinger equation whose solution directly yields the time-dependent charge density, current density, and a pulsating effective potential surface on which the process occurs. The new equation is also derived through Nelson's stochastic interpretation of the single-particle Schr\"odinger equation. A ``thermodynamics'' of the entire time-evolving system is suggested in terms of space- and time-dependent quantities. New algorithms have been devised for solving the above equation in one and two spatial dimensions, in a succession of time steps. Results have been obtained and analyzed in the approach regime for proton-neon high-energy (25-keV) collisions, which permit excitation but not ionization. These results show distinct nonlinear features.