To bypass the difficulty of solving the one-electron time-dependent Schrödinger equation in momentum space with the interacting nonlocal Coulomb potential, we have recently formulated an alternative accurate and efficient ab initio treatment (Ongonwou et al., Ann Phys 375:471, 2016; Ekogo et al., Phys Scr 97:115402, 2022), which relies on the expansion of the atomic wave function and the interacting nonlocal Coulomb potential on a discrete basis set of Coulomb Sturmian functions in momentum space. To further illustrate the validation and credibility of our proposed theoretical and numerical approaches, we study the above-threshold ionization of the hydrogen atom exposed to ultrashort infrared, ultraviolet, and low-and-high-frequency laser pulses. The energy spectra, momentum, angular distributions of the photoelectrons, and bound-state populations at the end of the laser pulse have been numerically evaluated, analyzed, and compared against predictions of other well-known time-dependent calculations in the literature. They are obtained either by using the ionized wave function or by projecting the total electron wave packets at the end of the laser pulse onto the continuum states constructed using the incoming Coulomb wave function. We explore the physical observables’ dependence on the carrier-envelope phase of the laser pulses. Our theoretical model captures the left–right dependence and breaks backward–forward symmetry in the emitted photoelectron momentum and angular distributions.

为了绕过在动量空间中求解具有相互作用的非局域库仑势的单电子时间相关薛定谔方程的困难，我们最近制定了一种替代的准确且高效的从头计算处理（Ongonwou 等人，Ann Phys 375:471, 2016） ；Ekogo 等人，Phys Scr 97:115402, 2022），它依赖于动量空间中库仑斯特米安函数的离散基组上原子波函数和相互作用的非局域库仑势的展开。为了进一步说明我们提出的理论和数值方法的有效性和可信度，我们研究了暴露于超短红外、紫外和低频和高频激光脉冲的氢原子的阈值以上电离。对能量谱、动量、光电子的角分布以及激光脉冲结束时的束缚态布居进行了数值评估、分析，并与文献中其他众所周知的时间相关计算的预测进行了比较。它们是通过使用电离波函数或通过将激光脉冲末端的总电子波包投影到使用传入库仑波函数构造的连续态上来获得的。我们探索了物理可观测量对激光脉冲的载波包络相位的依赖性。我们的理论模型捕捉了发射光电子动量和角分布的左右依赖性并打破了前后对称性。