Numerical solution of Dalgarno-Lewis equations by a mapped Fourier grid method

Abstract

Inhomogeneous radial differential equations emerging in applications of standard perturbation theory are numerically solved by a novel approach making use of Fourier grid methods in conjunction with a simple mapping scheme. The proposed algorithm is applied along the lines of the Dalgarno-Lewis method [Proc. R. Soc. London, Ser. A 223, 70 (1955)] to the calculation of the static dipole polarizabilities and hyperpolarizabilities of 1s, 2s, and 2p states of hydrogen atom and their frequency dependent dynamic dipole polarizabilities. The high efficiency and accuracy of the algorithm are demonstrated for the above test cases, where exact values are available. Then, the frequency dependent dipole polarizability of the ground state of lithium atom is computed by a variationally stable method combining an effective local potential approach with a second-order energy correction. The obtained results are in perfect agreement with other elaborate theoretical approaches.