Theoretical Study of antiproton dynamics in support of antihydrogen formation projects

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In the first three years, we developed a time-dependent wave packet formalism and a semiclassical scattering theory and applied them to the collision processes of hydrogen atoms, hydrogenic ions, negative hydrogen ions, helium atoms and hydrogen molecule ions with an antiproton. Total antiproton-capture cross sections were calculated with satisfactory accuracy but each partial cross section for a transition to a specific protonium state was not obtained by these methods. This is because the number of relevant channels amounts to several tens of thousand and the numerical calculations are impossible owing to the size of programming size and the CPU time. In the third year, Dr. Xiao-Min Tong joined the research group and the collaboration with Toshima lead to a novel scattering theory based on the causality relation of Green's function.. In this approach, only the scattered wave propagating outward is calculated and the boundary condition of the scattering equations is automatically satisfied without the tedious procedure of adjusting the wave functions at the asymptotic region. We succeeded in evaluating each partial cross section with high accuracy by this new method. Besides we have applied it to the negative-muon capture processes and the antiprotonic helium formation.For positronium formation processes, we developed a new approach in which the positronium formation and the pair annihilation in a unified manner introducing a optical potential for the annihilation. We also introduced the time-delay matrix for the analysis of overlapping resonances successfully.