Numerical Solutions of Dirac Equation with Coulomb and Vacuum Polarizaton Potentials

We wish to develop an efficient numerical method for solving a Dirac equation with Coulomb potential and various corrections,^[1,2] with the aim to calculate finite nuclear mass effects accordingly to HPQED theory. ^[3]These finite mass effects are usually neglected or treated very approximately, in particular for extended size nuclei. Here we show that the Dirac equation with Coulomb and vacuum polarization potentials for a point nucleus does not have normalizable solutions. Such solution exists only for extended size nuclei, which demonstrates that the extended nuclear size is essential for obtaining high precision results for binding energies.



[1] W. R. Johnson, ”Atomic Structure Theory”, 2005

[2] V. M. Shabaev, et al., Phys. Rev. Lett. , 2004

[3] K. Pachucki, V. A. Yerokhin, Phys. Rev. A , 2024