Applicability of the Dirac-Fock method combined with Core Polarization in calculations of alkali atoms

TL;DR

This work evaluates the local Dirac-Fock with core polarization (LDFCP) approach, embedded in a local Dirac-Hartree-Fock potential, for calculating static polarizabilities, blackbody-radiation Stark shifts, and the Bethe logarithm in alkali atoms. Using an effective one-electron model with a frozen core and a semi-empirical core-polarization potential, solved via a dual-kinetic-balance B-spline basis to yield a discrete pseudo-spectrum, the study computes $\alpha_0$, $\alpha_2$, and thermal Stark shifts at $T=300$ K, comparing with high-precision literature. The results show excellent agreement for scalar polarizabilities ($\sim$1% level) and reasonable tensor-polarizability behavior, but reveal that CP corrections degrade the accuracy of the Bethe logarithm for heavier alkalis, indicating CP corrections are suitable mainly for light systems. Overall, the method offers a fast, transferable route for polarizabilities and Stark shifts, while clarifying the limitations of LDFCP for relativistic QED quantities near the nucleus.

Abstract

In this work, we investigate the applicability of the core-polarization-corrected Dirac--Fock method, formulated within the framework of the local Dirac--Hartree--Fock (LDF) potential, for the accurate determination of static scalar and tensor electric dipole polarizabilities. This work presents theoretical values of blackbody-radiation-induced Stark shifts of atomic energy levels. The Dirac--Fock method augmented by core-polarization corrections is employed not only to evaluate these shifts but also to compute the Bethe logarithm for alkali-metal atoms. The results are critically compared with data available in the contemporary literature, and the strengths and limitations of the present approach are discussed.

Figures (1)

• Figure 1: Thermal one-loop correction to the self-energy of an atomic electron at an arbitrary level $a$. Double line means the bound electron states in the Furry picture, the wavy line refers to the photon propagator. The notation $\gamma_T$ indicates that the thermal photon propagator is considered DHRDon.