Calculation of energy loss in antiproton collisions with many-electron systems using Ehrenfest's theorem

Abstract

Energy loss in collisions of charged projectiles with many-electron systems can be dealt with in time-dependent density functional theory by invoking Ehrenfest's theorem for the time evolution of expectation values of observables. We derive an exact expression for the evaluation of energy loss for systems described in a target reference frame, which is a functional of the electron density. Using an approximation scheme, we then apply the expression to antiproton-atom collisions at intermediate and high energies within the framework of the basis generator method. The calculations are performed within the semiclassical approximation for the nuclear motion, and a straight-line trajectory is employed. The energy loss is evaluated from an expectation value of the time derivative of the time-dependent projectile potential, and it avoids the problem of identifying the excited and ionized many-electron contributions in the many-electron wave function. There is also no need to invoke the independent-event model, since the calculations are performed within the framework of the independent-electron mean-field model. Detailed comparisons are provided for net ionization and total energy loss of antiprotons colliding with hydrogen, helium, neon, carbon, nitrogen, and oxygen. Reasonable agreement is found with the results from one-electron and two-electron calculations for atomic hydrogen and helium, and with experiment in the latter case. For the $\overline{p}\text{\ensuremath{-}}\mathrm{Ne}$ system at intermediate collision energies, we find discrepancies with previous work that included only single-electron transitions. The sequence of results for C, N, O, and Ne allows one to paint a consistent picture that awaits experimental verification.