Clarify sources of residual deviations in K-shell binding energies under Coulomb–Casimir modeling

Determine whether the residual deviations between calculated K-shell binding energies—obtained by solving the Dirac equation with the combined Coulomb–Casimir potential and first-order perturbation correction—and the experimental literature values can be reduced by incorporating additional nuclear multipole moments beyond the quadrupole term (such as octupole and higher-order moments) or by modeling more complex deviations of the nuclear surface from spherical symmetry, or whether other unaccounted physical effects are responsible for these discrepancies.

Background

The paper introduces a modification to the electron–nucleus interaction by adding a Casimir-effect-derived term to the Coulomb potential, then solves the Dirac equation for K-shell electrons. Using first-order perturbation theory, the authors compare the resulting binding energies to spectroscopic literature values across the periodic table. They include nuclear shape effects via the quadrupole moment as a first approximation.

Figure 1 shows that including the Casimir contribution substantially improves agreement for heavy elements, yet residual discrepancies remain for several elements. The authors explicitly state that it is unresolved whether these deviations can be removed by adding higher-order nuclear multipole moments or more sophisticated nuclear shape models, or if additional physical effects must be considered.