Dirac方程的数值解法及其在原子总能量计算中的应用

中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.

A numerical method for solving dirac equation and its application to calculation of total atomic energy

The solution to radial Dirac equation is fundamental to relativistic atomic(ionic) structure calculation in the centrally symmetric potential approximation.This paper presents a numerical method for solving the radial Dirac equations by virtue of the analogy between the large component of relativistic radial wave functions and non-relativistic ones.Firstly,for the validation of the method,numerical solutions for a hydrogen-like potential are compared with exact analytical solutions.Then,this numerical method is extended to solve relativistic atomic structure based on analytical potentials. The results show that the total atomic(ionic) energies provided by numerical method agree with experimentally measured values and those given by other methods.