Theoretical study on resonance states and photoionization processes with the combination of complex coordinate method and analytical derivative method

复坐标法是一种直接计算共振态能级和寿命的理论方法。本研究为计算原子和分子的光致电离截面提供了一种有效的理论方法。为了解决以前的计算方案中一个长期存在的问题，即难以选择合适的基函数，我们建议利用解析法计算的极化率的一阶和二阶导数，对复轨道指数的随频率变化的极化率进行变分优化。

The complex coordinate method is a theoretical method to evaluate directly both the energy level and lifetime of resonance states. This study develops an efficient theoretical method to evaluate atomic and molecular photoionization cross sections. To solve a long-standing problem in the previous calculation scheme, which is the difficulty in selecting appropriate basis functions, we propose to variationally optimize the frequency-dependent polarizability with respect to complex orbital exponents, with using analytically evaluated first and second derivatives of the polarizability.