Photoionization of atoms and molecules studied by the Crank-Nicolson method
Photoionization of atoms and molecules studied by the Crank-Nicolson method
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DOI：
10.1103/physreva.90.033403
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发表时间：
2014-09-04
影响因子：
2.9
通讯作者：
Bian, Xue-Bin
中科院分区：
文献类型：
--
作者：
Bian, Xue-Bin
Crank-Nicolson（C-N）方法与B样条基组相结合，可用于原子和分子光电离截面的含时和不含时计算。对于非定常系统，时间-时间传播（ITP）方法通常只能将任意初始状态直接收敛到基态。与现有方法不同，C-N方法通过控制时间步长，不仅可以将任意初始态直接收敛到基态，而且可以将激发态和连续态直接收敛到基态。这是非常有用的，如果一个感兴趣的只是一部分的光谱信息，因为计算是相对便宜的。C-N方法也可以直接应用于含时计算。在时间演化过程中，通过将波函数投影到ITP方法得到的本征态上，可以得到能量和动量等谱信息。与时间相关和与时间无关的计算都与以前的结果吻合得很好。该方法也可直接推广到双电子体系。
The Crank-Nicolson (C-N) method combined with a B-spline basis set can be used in both time-dependent and time-independent calculations of the photoionization cross sections of atoms and molecules. For time-independent systems, the imaginary-time propagation (ITP) method can usually only converge an arbitrary initial state to the ground state directly. Contrary to existing methods, it is found that the C-N method can converge an arbitrary initial state directly to not only the ground state but also excited and continuum states by controlling the time-step size. It is very useful if one is interested in only part of the spectral information since the computation is relatively cheap. The C-N method can also be directly applied in time-dependent calculations. During the time evolution, the spectral information, such as energy and momentum, can be retrieved by projecting the wave function on the eigenstates obtained using the ITP method. Both time-dependent and time-independent calculations agree very well with previous results. This method can also be extended to two-electron systems directly.