Dual kinetic balance approach to basis set expansions for the Dirac equation

Abstract

A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.

14 pages, 1 table

References in corpus (7)

• Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$
• Recoil correction to the bound-electron g factor in H-like atoms to all orders in $\alpha Z$
• Two-electron self-energy contribution to the ground state energy of heliumlike ions
• Nuclear recoil corrections to the $2p_{\frac{3}{2}}$ state energy of hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$
• Vacuum polarization screening corrections to the ground state energy of two-electron ions
• Evaluation of the low-lying energy levels of two- and three-electron configurations for multi-charged ions
• Evaluation of the two-photon exchange diagrams for the $(1s{)}^{2}2p_{3/2}$ electron configuration in Li-like ions

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