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

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 cycleʹs 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.