Peng Liang-You, Starace Anthony F
Department of Physics and Astronomy, The University of Nebraska-Lincoln, Nebraska 68588-0111, USA.
J Chem Phys. 2006 Oct 21;125(15):154311. doi: 10.1063/1.2358351.
We present an efficient and accurate grid method for solving the time-dependent Schrodinger equation for an atomic system interacting with an intense laser pulse. Instead of the usual finite difference (FD) method, the radial coordinate is discretized using the discrete variable representation (DVR) constructed from Coulomb wave functions. For an accurate description of the ionization dynamics of atomic systems, the Coulomb wave function discrete variable representation (CWDVR) method needs three to ten times fewer grid points than the FD method. The resultant grid points of the CWDVR are distributed unevenly so that one has a finer grid near the origin and a coarser one at larger distances. The other important advantage of the CWDVR method is that it treats the Coulomb singularity accurately and gives a good representation of continuum wave functions. The time propagation of the wave function is implemented using the well-known Arnoldi method. As examples, the present method is applied to multiphoton ionization of both the H atom and the H(-) ion in intense laser fields. The short-time excitation and ionization dynamics of H by an abruptly introduced static electric field is also investigated. For a wide range of field parameters, ionization rates calculated using the present method are in excellent agreement with those from other accurate theoretical calculations.
我们提出了一种高效且精确的网格方法，用于求解与强激光脉冲相互作用的原子系统的含时薛定谔方程。与常用的有限差分（FD）方法不同，径向坐标采用由库仑波函数构建的离散变量表示（DVR）进行离散化。为了准确描述原子系统的电离动力学，库仑波函数离散变量表示（CWDVR）方法所需的网格点数比FD方法少三到十倍。CWDVR产生的网格点分布不均匀，使得在原点附近有更精细的网格，而在较大距离处有更粗的网格。CWDVR方法的另一个重要优点是它能精确处理库仑奇点，并能很好地表示连续波函数。波函数的时间传播采用著名的阿诺尔迪方法实现。作为示例，本方法应用于强激光场中H原子和H(-)离子的多光子电离。还研究了突然引入的静电场对H的短时激发和电离动力学。对于广泛的场参数范围，使用本方法计算的电离率与其他精确理论计算的结果非常吻合。
