An approximation to the Lamb shift and hyperfine splitting as nonlinear effective Coulomb-like interactions in the Dirac equation

库仑定律修正对氢原子Lamb移位的贡献

Input of the Coulomb law modification to the Lamb shift of the hydrogen atom

本文基于库仑势Dirac方程精确解的新方法，计算了导致库仑定律修正的辐射修正，进而获得了氢原子能谱并计算了最低能态的Lamb移位。

Use of Lambert's Theorem for the n-Dimensional Coulomb Problem

We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and which allows us to treat the system as an essentially one dimensional problem. The semiclassical result assumes a simple analytical form and is well suited for a numerical evaluation. The method can also be extended to classically forbidden space regions. Already for moderately large principal quantum numbers nu >= 5, the semiclassical Green function is found …

Two fermion relativistic bound states: hyperfine shifts

We discuss the hyperfine shifts of the Positronium levels in a relativistic framework, starting from a two fermion wave equation where, in addition to the Coulomb potential, the magnetic interaction between spins is described by a Breit term. We write the system of four first order differential equations describing this model. We discuss its mathematical features, mainly in relation to possible singularities that may appear at finite values of the radial coordinate. We solve the boundary value problems both in the singular and non singular cases and we develop a perturbation scheme, well suite…

Exact two-loop vacuum polarization correctionto the Lamb shift in hydrogen-like ions

We present a calculation scheme for the two-loop vacuum polarization correction of order $α^2$ to the Lamb shift of hydrogen-like high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in $(Zα)$. By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuum polarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- an…

A Coupled Cluster Theory Based on Quantum Electrodynamics

An electrodynamical coupled cluster (CC) methodology starting from a covariant formalism and an equal time approximation, and finally based on the Dirac-Fock picture of the electron and positron fields and Coulomb gauge, is given here. The formalism first leads to different physical interactions from the use of an exponential cluster operator for radiative effects. Lamb, Breit and hyperfine interactions are obtained. Next, relativistic many-body effects are determined using the matter cluster in a way familiar from the nonrelativistic CC. This step can be nontrivial. By allowing the matter clu…

Collective magnetic splitting in single-photon superradiance

In an ensemble of identical atoms, cooperative effects like sub- or superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multi-level systems are more difficult to handle. In this work we show that in a system of atoms or nuclei under the action of an external magnetic field, the collective contribution to the level shifts can amount to seizable deviations from the single-atom Zeeman or magnetic hyp…