Related papers: Analytical formula for the Uehling potential
The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the…
Properties and different representations of the Uehling potential are investigated. Based on these properties and by using our formulas for the Fourier transform of the Uehling potential we have developed the new analytical, logically…
A number of properties of the Uehling potential are investigated. In particular, we determine the Fourier spatial resolution of the Uehling potential. The lowest-order correction on vacuum polarisation is re-written in terms of the electron…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
The shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen. A parametric hadronic polarization function obtained from experimental cross sections…
We consider a correction to energy levels in a pionic atom induced by the Uehling potential, i.e., by a free electron vacuum-polarization loop. The calculation is performed for circular states (l=n-1). The result is obtained in a closed…
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions $K_{0}(b r)$ and $K_{1}(b r)$. This central…
Radiative corrections to electronic structure are characterized by perturbative expansions in $\alpha$ and $Z\alpha$, where $\alpha$ is the fine-structure constant and $Z$ is the nuclear charge. A formulation of the leading-order…
The vacuum-polarization correction for bound electrons or muons is examined. The objective is to formulate a framework for calculating the correction from bound-state quantum electrodynamics entirely in coordinate space, including the…
Effects of vacuum polarization modify the energy levels in atoms with an orbiting particle heavier than an electron. The dominant effect is due to the Uehling potential. In this paper we consider the relativistic corrections to the energy…
We perform a theoretical study of vacuum polarization corrections to the hyperfine structure in many-electron atoms. Calculations are performed for systems of interest for precision atomic tests of fundamental physics belonging to the…
Vacuum polarization corrections to the energy levels of bound electrons are calculated using a perturbative path integral formalism. We apply quantum electrodynamics in a framework which treats the strong binding nuclear field to all…
The Uehling correction to the energy levels is presented in terms of the hypergeometric functions 2F1. This presentation allows to derived various asymptotics and approximations. Further applications of this method to other atomic…
We present calculations of the one-loop vacuum polarization correction (Uehling potential) for the three-body problem in the NRQED formalism. The case of one-electron molecular systems is considered. Numerical results of the vacuum…
We outline a general formalism for treating vacuum polarization phenomena within an effective field expansion. The coupling between source charges and virtual fields is examined from the perspectives of electrostatic potentials, induced…
Complete vacuum polarization calculations incorporating finite nuclear size are presented for hydrogenic ions with principal quantum numbers n=1-5. Lithiumlike, sodiumlike, and copperlike ions are also treated starting with Kohn-Sham…
We present analytical formulas for the vacuum-polarization Uehling potential in the case where the finite size of the nucleus is modeled by a Fermi charge distribution. Using a Sommerfeld-type development, the potential is expressed in…
The hadronic vacuum polarization correction to the $g$ factor of a bound electron is investigated theoretically. An effective hadronic Uehling potential obtained from measured cross sections of $e^- e^+$ annihilation into hadrons is…
A formula for potential U of the He-4--He-4 interaction in the liquid state is obtained by the direct electromagnetic computation as a function of the interatomic distance R. The potential decreases exponentially at large R. The further…
The Uehling contribution to the Lamb shift can be computed exactly in terms of the Uehling potential function. However derivations of this function are complex involving avoiding divergences using intricate techniques from early quantum…