2007/10/16 by Kyle Beloy, K. Beloy, Andrei Derevianko
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Nuclear physics research studies #physics.atom-ph
paper · pdf · doi:10.1016/j.cpc.2008.03.004
published as Computer Phys. Comm. 179, 310 (2008) · 10 pages
arxiv created 2007/10/16 · openalex publication_date 2008/03/15 · arxiv updated 2011/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)] is extended to problems with a non-local spherically-symmetric Dirac-Hartree-Fock potential. We implement the DKB method using B-spline basis sets and compare its performance with the widely-employed approach of Notre Dame (ND) group [W.R. Johnson and J. Sapirstein, Phys. Rev. Lett. 57, 1126 (1986)]. We compare the performance of the ND and DKB methods by computing various properties of Cs atom: energies, hyperfine integrals, the parity-non-conserving amplitude of the 6s1/2-7s1/2 transition, and the second-order many-body correction to the removal energy of the valence electrons. We find that for a comparable size of the basis set the accuracy of both methods is similar for matrix elements accumulated far from the nuclear region. However, for atomic properties determined by small distances, the DKB method outperforms the ND approach. In addition, we present a strategy for optimizing the size of the basis sets by choosing progressively smaller number of basis functions for increasingly higher partial waves. This strategy exploits suppression of contributions of high partial waves to typical many-body correlation corrections.