原子与动态核的瑞利散射
Rayleigh Scattering at Atoms with Dynamical Nuclei
摘要：
在总能量低于原子电离阈值的系统态子空间上研究了光子与动态原子核的散射（瑞利散射）。电子和原子核的运动学被选择为非相对论性的，它们的自旋被忽略。在氢原子或单电子离子与量子化辐射场相互作用的简化模型中，忽略光子的螺旋性，在光子能量很高和光子能量低于任意小但固定的能量（红外截止）时，光子与电子和原子核之间的相互作用被关闭，严格地建立了瑞利散射的渐近完备性.在证明这一结果的过程中，我们发现，在将电子和原子核与光子耦合之后，只要原子的质心速度小于光速，原子仍然具有稳定的基态;但是原子的激发态转变为共振态。渐近完备性的证明，然后从扩展的积极换向器的方法和传播估计的原子和光子在以前的文件。本文提出的方法可以推广到更现实的模型。然而，目前还不知道如何去除红外截止。
英文摘要：
Scattering of photons at an atom with a dynamical nucleus is studied on the subspace of states of the system with a total energy below the threshold for ionization of the atom (Rayleigh scattering). The kinematics of the electron and the nucleus is chosen to be non-relativistic, and their spins are neglected. In a simplified model of a hydrogen atom or a one-electron ion interacting with the quantized radiation field in which the helicity of photons is neglected and the interactions between photons and the electron and nucleus are turned off at very high photon energies and at photon energies below an arbitrarily small, but fixed energy (infrared cutoff), asymptotic completeness of Rayleigh scattering is established rigorously. On the way towards proving this result, it is shown that, after coupling the electron and the nucleus to the photons, the atom still has a stable ground state, provided its center of mass velocity is smaller than the velocity of light; but its excited states are turned into resonances. The proof of asymptotic completeness then follows from extensions of a positive commutator method and of propagation estimates for the atom and the photons developed in previous papers. The methods developed in this paper can be extended to more realistic models. It is, however, not known, at present, how to remove the infrared cutoff.
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