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New numerical method for the solutions of the MCDF equations based on the CIP method

机译：基于CIP方法求解MCDF方程的新数值方法

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摘要

A new numerical method based on the constrained interpolation profile (CIP) method to solve the Multiconfiguration Dirac-Fock (MCDF) equations is presented. The radial wave functions are represented by the values and the spatial derivatives on an arbitrary grid system, and approximated by cubic polynomials. Owing to this representation, the values and the spatial derivatives of the effective charge distribution and inhomogeneous term are calculated using the previous cycle's wave functions. Then the homogeneous MCDF equations are integrated to obtain two linearly independent solutions, which are used to construct the Green function, by the adaptive stepsize controlled Runge-Kutta method controlling the truncation errors within a prescribed accuracy. The radial wave function is improved by taking the convolution of the Green function and the inhomogeneous term. The effectiveness of this numerical procedure is investigated after implementing it into the relativistic atomic structure code GRASP92.
机译：提出了一种基于约束插值轮廓（CIP）方法求解多配置狄拉克-福克（MCDF）方程的新数值方法。径向波函数由任意网格系统上的值和空间导数表示，并由三次多项式近似。由于这种表示，有效电荷分布和非均匀项的值和空间导数是使用前一个周期的波动函数计算的。然后，将齐次的MCDF方程进行积分，以获得两个线性独立的解决方案，这些解决方案用于通过将分段误差控制在规定的精度范围内的自适应步长控制的Runge-Kutta方法来构造Green函数。通过采用格林函数和不均匀项的卷积来改善径向波函数。在将其实现为相对论原子结构代码GRASP92之后，将研究此数值过程的有效性。

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