Theoretical Study of antiproton dynamics in support of antihydrogen formation projects

在前三年中，我们发展了含时波包理论和半经典散射理论，并将它们应用于氢原子、类氢离子、负氢离子、氦原子和氢分子离子与反质子的碰撞过程。总的反质子捕获截面计算具有令人满意的精度，但每个部分截面的过渡到一个特定的质子状态，没有得到这些方法。这是因为相关通道的数量达到数万个，并且由于编程大小和CPU时间的大小，不可能进行数值计算。第三年，童晓敏博士加入研究小组，与丰岛合作，提出了基于绿色函数因果关系的新散射理论。在这种方法中，只计算向外传播的散射波，并且散射方程的边界条件自动满足，而无需在渐近区域调整波函数的繁琐过程。我们成功地评估每个部分截面与高精度的这种新方法。此外，我们还将其应用到负μ子俘获过程和反质子氦的形成过程中，对于正电子偶素的形成过程，我们发展了一种新的方法，将正电子偶素的形成和对湮灭统一起来，引入了一个用于湮灭的光学势.我们还成功地引入了用于重叠共振分析的时滞矩阵。

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.