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

2023/10/13 by A. Bağcı, Bağcı, A., Philip E. Hoggan +1
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic Physics (physics.atom-ph) #Atomic and Molecular Physics #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2310.09111

openalex publication_date 2023/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the use of Slater-type spinor orbitals in Dirac-Hartree-Fock method. Results for hydrogen-like atoms with super-critical nuclear charge
• Derivation of a four-spinor Dirac-like equation for the helium atom and an approximate ground state solution
• Spin-1/2 square-root operator equation with Coulomb potential - a perturbation analysis
• Relativistic exponential-type spinor orbitals and their use in many-electron Dirac equation solution
• Approximating Hamiltonian for Hartree-Fock solutions for nonrelativistic atoms