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Mini-workshop on "Numerical challenges in relativistic quantum mechanics"
Organizers: Werner Kutzelnigg (Bochum), Eric Séré (Paris-Dauphine)


Ingvar Lindgren (Göteborg, Sweden): "Energy-dependent perturbation theory: Combining quantum-electrodynamics with electron correlation"
Friday 19 April 2013, 11:45 - 12:30
Amphi Hermite



Large experimental efforts are now being made in studying highly charged ions, e.g., at GSI in Darmstadt, where the big FAIR facility is under construction. QED effects are also studied by precision laser or X-ray spectroscopy. One purpose of these works is to test the theory of quantum-electrodynamics (QED) under extreme conditions by comparing with accurate theoretical results. Signifcant discrepancies between theory and experiment have been reported, and more accurate calculations may reveal whether these are real or not. The most accurate procedures presently used for calculations on simple atomic systems are :

1. all-order many-body perturbative expansion with added analytical QED energy corrections, and :

2. two-photon QED calculations.

These methods have the shortcoming that they do not take into account the combination of QED and correlational effects. We have developed a third procedure, based upon energy-dependent perturbative theory, which for the first time makes it possible to include energy-dependent QED effects directly into the atomic wave function. This will improve the accuracy compared to methods currently in use.

The calculations are performed using the Coulomb gauge, which is most appropriate for the combined effect. Since QED effects, like the Lamb shift, have never been calculated in that gauge, this has required some development. This is now being implemented in our computational procedure, and some numerical results will be presented.