Solution of the Dirac–Coulomb equation using the Rayleigh–Ritz method: Results for He-like atoms

Abstract

The Dirac–Coulomb equation for helium-like ions is solved using the iterative self-consistent field method, with Slater-type spinor orbitals as the basis. These orbitals inherently satisfy the kinetic-balance condition due to their coupling for both large and small components. The 1/r12 Coulomb interaction is treated without constraints. Computations are carried out for total energies of atoms with nuclear charges up to Z ≤ 80 using both minimal and extended basis sets. Variationally optimal values for orbital parameters are determined through the Rayleigh–Ritz variational principle. No manifestations related to the Brown–Ravenhall disease are found. © 2024 Elsevier Inc.