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arXiv · 2310.09111

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

A. Bağcı·P. E. Hoggan
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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 $1/r_{12}$ Coulomb interaction is treated without constraints. Computations are carried out for total energies of atoms with nuclear charges up to $Z \leq 80$ 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.

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A. Bağcı, P. E. Hoggan. 2023-10-13. Solution of the Dirac-Coulomb equation using the Rayleigh-Ritz method. Results for He-like atoms. https://arxiv.org/abs/2310.09111

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