Ion and Electron Momentum Distributions from Single and Double Ionization of Helium Induced by Compton Scattering.

We present the momentum distributions of the nucleus and of the electrons from double ionization of the helium atom by Compton scattering of photons with hν=40 keV. We find that the doubly charged ion momentum distribution is very close to the Compton profile of the nucleus in the ground state of the helium atom, and the momentum distribution of the singly charged ion to give a precise image of the electron Compton profile. To reproduce these results, nonrelativistic calculations require the use of highly correlated initial- and final-state wave functions.

Agreement of Experiment and Theory on the Single Ionization of Helium by Fast Proton Impact.

Even though the study of ion-atom collisions is a mature field of atomic physics, large discrepancies between experiment and theoretical calculations are still common. Here we present experimental results with high momentum resolution on the single ionization of helium induced by 1-MeV protons, and we compare these to theoretical calculations. The overall agreement is strikingly good, and even the first Born approximation yields good agreement between theory and experiment. This has been expected for several decades, but so far has not been accomplished. The influence of projectile coherence effects on the measured data is briefly discussed in terms of an ongoing dispute on the existence of nodal structures in the electron angular emission distributions.

Two-dimensional oscillator in time-dependent fields: comparison of some exact and approximate calculations.

Operator-difference multilayer schemes for solving the time-dependent Schrödinger equation up to sixth order of accuracy in the time step are presented. Reduced schemes for solving a set of coupled time-dependent Schrödinger equations with respect to the hyper-radial variable are devised using expansion of a wave packet over the set of appropriate basis angular functions. Further discretization of the resulting problem is realized by means of the finite-element method. The convergence of the expansion with respect to the number of basis functions and the efficiency of the numerical schemes are demonstrated in the exactly solvable model of an electric-field-driven two-dimensional oscillator (or a charged particle in a constant uniform magnetic field), in which we explicitly observed an effect of the periodical focusing and defocusing of the probability density flux.