Speaker
Description
The accurate computation of QED corrections to the energy levels of heavy atoms and molecules poses a significant challenge. At the one-loop level the corrections to the electron-nucleus interaction are the vacuum polarization and the electron self-energy. The leading-order (in $Z\alpha$) vacuum polarization correction can be included in molecular computations as an effective local potential (Uehling potential) [1]. However, higher order corrections become increasingly complex. Recently the complete many-potential vacuum polarization density has been evaluated in the finite-basis approximation [2]. Self-energy on the other hand emerges as a non-local interaction, making its rigorous evaluation more involved. The main difficulty in both cases is applying an efficient renormalization scheme to obtain accurate results without loss of precision due to numerical cancellations. Additionally, in order to extend the approach towards more complex systems, it must comply with the well-established framework for many-electron systems. In this contribution we present a method where the solutions of the external-Coulomb-field Dirac equation are expanded in a finite Gaussian basis set, and the partial wave renormalization scheme [3,4,5] is applied to the self-energy problem of hydrogen-like atoms. The unrenormalized bound self-energy is evaluated for each set of intermediate states with a given $\kappa$ quantum number separately. The mass renormalization counterterm for each partial wave is treated on equal footing in a finite-basis, avoiding the need for the analytical solutions and complicated multi-dimensional or complex-contour numerical integration. With each term being finite in the partial wave expansion, the UV regulator can be removed to obtain a finite contribution. Our numerical approach shows good agreement with the results of Quiney and Grant, using a numerical complex-contour integral scheme [5].
[1] A. Sunaga, M. Salman, and T. Saue. 4-component relativistic Hamiltonian with effective QED potentials for molecular calculations. J. Chem. Phys. 157, 164101 (2022).
[2] M. Salman and T. Saue. Calculating the many-potential vacuum polarization density of the Dirac equation in the finite-basis approximation. Phys. Rev. A 108, 012808 (2023).
[3] I. Lindgren, H. Persson, S. Salomonson, and A. Ynnerman. Bound-state self-energy calculation using partial-wave renormalization. Phys. Rev. A 47, R4555(R) (1993).
[4] H. M. Quiney and I. P. Grant. Partial-wave mass renormalization in atomic QED calculations. Phys. Scr. 132 (1993).
[5] H. M. Quiney and I. P. Grant. Atomic self-energy calculations using partial-wave mass renormalization. J. Phys. B: At. Mol. Opt. Phys. 27 L299 (1994).
