相关论文: Analytical matrix elements of the Uehling potentia…
The closed analytical expression for the Uehling potential is derived. The Uehling potential describes the lowest-order correction on vacuum polarisation in atomic and muon-atomic systems. We also derive the analytical formula for the…
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…
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…
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…
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…
Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix elements of the generalized Yukawa potential with complex screening…
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…
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 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…
Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic 205 Bi, 147 Sm, and 89 Zr are presented. The hyperfine structure due to magnetic dipole and electric…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
The energy levels of the $n=1$ and $n=2$ bound states of the $\mu^+\mu^-$ atom (true muonium) are calculated starting from a previously derived potential that correctly describes positronium to order $\alpha^5$ supplemented by the known…
A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…
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…
The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions…
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…
A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional…
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…