Gersbacher Rolf, Broad John T
University of Applied Sciences Esslingen, Robert Bosch Str. 1, 73037, Göppingen, Germany.
Sci Rep. 2022 Jul 1;12(1):11155. doi: 10.1038/s41598-022-14706-9.
The J-Matrix approach for scattering is extended to the time-dependent Schrödinger equation (TDSE) for one electron atoms in external few cycle attosecond fields. To this purpose, the wave function is expanded in square integrable ([Formula: see text]) Sturmian functions and an equation system for the transition amplitudes is established. Outside the interaction zone, boundary conditions are imposed at the border in the [Formula: see text] function space. These boundary conditions correspond to outgoing waves (Siegert states) and minimize reflections at the [Formula: see text] boundary grid. Outgoing wave behaviour in the asymptotic region is achieved by employing Pollaczek functions. The method enables the treatment of light - atom interactions within arbitrary external fields. Using a partial wave decomposition, the coupled differential equation system is solved by a Runge-Kutta method. As a proof of the method ionization processes of atomic hydrogen in half and few cycle attosecond fields are examined. The electron energy spectrum is calculated and the numerical implementation will be presented. Different forms of the interaction operator are considered and the convergence behaviour is discussed. Results are compared to other studies which use independent approaches like finite difference methods. Remarkable agreement is achieved even with strong field strengths of the electromagnetic field. It is demonstrated that expanding in [Formula: see text] functions and imposing boundary conditions at the limit in the [Formula: see text] function space can be an advantageous alternative to conventional propagation methods using complex absorbing potentials or complex scaling.
用于散射的J矩阵方法被扩展到用于描述处于外部少周期阿秒场中的单电子原子的含时薛定谔方程（TDSE）。为此，波函数在平方可积（[公式：见正文]）的斯图姆函数中展开，并建立了一个用于跃迁振幅的方程组。在相互作用区域之外，在[公式：见正文]函数空间的边界处施加边界条件。这些边界条件对应于出射波（西格特态），并使在[公式：见正文]边界网格处的反射最小化。通过采用波拉克泽克函数来实现渐近区域中的出射波行为。该方法能够处理任意外部场中的光 - 原子相互作用。利用分波分解，通过龙格 -库塔方法求解耦合微分方程组。作为该方法的一个验证，研究了原子氢在半周期和少周期阿秒场中的电离过程，并计算了电子能谱，还将展示数值实现过程。考虑了相互作用算符的不同形式并讨论了收敛行为。将结果与其他使用有限差分法等独立方法的研究进行了比较。即使在电磁场强度很强的情况下，也取得了显著的一致性。结果表明，在[公式：见正文]函数中展开并在[公式：见正文]函数空间的极限处施加边界条件，可能是使用复吸收势或复标度的传统传播方法的一种有利替代方法。
