Theoretical studies of few-body problems
"Heavy ion collisions with atomic and molecular targets produce many outcomes. The Schrödinger equation is not analytically soluble for more than two mutually interacting particles. As a result, theory must resort to using approximations, the validity of which is determined by comparison with experiment. This work is focused on finding better approximations to describe ionization and capture processes in proton collisions. Proton-impact ionization of molecular hydrogen is treated as a 3-body problem. Usually the target is treated as an atomic target and the results are multiplied by an ad hoc factor to account for the molecular structure. Measured cross sections for proton-molecular hydrogen scattering shows structure which could be attributed to a two-center interference effect similar to the classical Young's double slit interference. Three-body fully quantum mechanical M3DW-EIS (molecular 3-body distorted wave Eikonal initial state) results are presented here which, for the first time, properly treats the target as a molecule and which predicts the same structure. Single charge transfer, transfer with target excitation, and double capture for proton-helium collisions is also examined. For the charge transfer process it's a challenge to correctly predict the magnitude and the shape of the fully differential cross sections (FDCS). In the case of transfer excitation the fully quantum mechanical model 4BTTE (4-body transfer with target excitation) was used to calculate the FDCS. It overestimates the absolute experimental FDCS measurements at all energies. A new model is introduced which includes all two-particle interactions in the final state exactly. This model produces better agreement with the experimental data than the 4BTTE model"--Abstract, page iv.
Missouri University of Science and Technology
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