We study and develop the stationary scattering theory for a class of one-body Stark Hamiltonians with short-range potentials, including the Coulomb potential, continuing our study in Adachi et al. (JDE 268: 5179–5206, 2020; Stationary scattering theory for 1-body Stark operators). The classical scattering orbits are parabolas parametrized by asymptotic orthogonal momenta, and the kernel of the (quantum) scattering matrix at a fixed energy is defined in these momenta. We show that the scattering matrix is a classical type pseudodifferential operator and compute the leading order singularities at the diagonal of its kernel. Our approach can be viewed as an adaption of the method of Isozaki-Kitada (Tokyo Univ. 35: 81–107, 1985) used for studying the scattering matrix for one-body Schrödinger operators without an external potential. It is more flexible and more informative than the more standard method used previously by Kvitsinsky-Kostrykin (Teoret. Mat. Fiz. 75(3): 416-430, 1988) for computing the leading order singularities of the kernel of the scattering matrix in the case of a constant external field (the Stark case). Our approach relies on Sommerfeld’s uniqueness result in Besov spaces, microlocal analysis as well as on classical phase space constructions.

我们研究并发展了一类具有短程势的单体斯塔克哈密顿量的平稳散射理论，包括库仑势，继续我们在 Adachi 等人的研究。(JDE 268: 5179–5206, 2020; 1-body Stark 算子的稳态散射理论)。经典散射轨道是由渐近正交动量参数化的抛物线，固定能量下的（量子）散射矩阵的核定义在这些动量中。我们证明散射矩阵是经典类型的伪微分算子，并计算其内核对角线上的前导奇点。我们的方法可以看作是对 Isozaki-Kitada (Tokyo Univ. 35: 81–107, 1985) 方法的改编，该方法用于研究没有外部势的单体薛定谔算子的散射矩阵。与 Kvitsinsky-Kostrykin (Teoret. Mat. Fiz. 75(3): 416-430, 1988) 之前使用的用于计算散射矩阵核的前导奇异点的标准方法相比，它更灵活、信息量更大恒定外场的情况（斯塔克情况）。我们的方法依赖于 Sommerfeld 在 Besov 空间、微局域分析以及经典相空间构造中的唯一性结果。