Nonlinear dynamics in proton-noble gas atom collisions

Abstract

Some recent works from our laboratory on time-dependent (TD) quantum-fluid density-functional studies of high-energy (25 keV) proton-neon and proton-helium atom collisions have been reviewed. These results in two generalized non-linear Schrodinger equations (GNLSE), depending on the forms of the various density functionals employed. The numerical solutions of these equations yield various time dependent quantities in three-dimensional space, e.g., electronic charge density, current density, difference density, effective potential surface as well as TD induced dipole moment, dipole polarizability, etc. The approach enables one to follow a collision process from start to finish, in course of time, thereby providing fresh insights into the mechanism of a collision process and identifying the non-linear features, if any, of the process which permits excitation but not ionization. One of the most interesting observations in this study is a natural partitioning of the collision process into <em>approach, encounter </em>and, <em>departure </em>regimes. Our approach has involved a simultaneous consideration of three crucial problems in density-functional theory, namely, time-dependence, excited states and a satisfactory kinetic energy density functional. Further, the phase associated with the hydrodynamic "wave function" has been related to Berry's geometrical phase in quantum mechanics.