三体色散散射

摘要：

本文研究了三体色散系统的光谱和散射理论，其中包括一个无质量粒子和一个两体非相对论对，以及三个粒子之间的两体短相互作用。我们证明了局部衰减估计和传播估计，然后用于证明系统的所有非阈值负能量的渐近完备性。通过添加（迹类）非粒子守恒相互作用，这也模拟了电离过程。特别是，如果无质量粒子仅通过非粒子数守恒相互作用相互作用，如果系统的总能量为负，则不可能电离，正如光电效应的形式分析所预测的那样。

英文摘要：

We study the spectral and scattering theory of three body dispersive systems, which include a massless particle and a two body non-relativistic pair, along with two body short interactions among the three particles. We prove local decay estimates and propagation estimates, which are then used to prove asymptotic completeness for all non-threshold negative energies of the system. By adding (trace class) non-particle-conserving interactions, this models ionization processes as well. In particular, if the massless particle is interacting only through the non-particle-number conserving interactions, no ionization is possible if the total energy of the system is negative, as predicted by the formal analysis of the photo-electric effect.

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