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QED dans les ions à un et deux électrons : états très excités ou quasi-dégénérés

Abstract : We present theoretical and numerical evaluations of
the contributions of quantum electrodynamics (QED) to the energy
levels of one- and two-electron ions.

First, we give an overview of energy level measurements in simple
systems composed of a nucleus and a few electrons (especially hydrogen,
helium, and hydrogen- and helium-like ions, including highly-charged
ions). Such energy levels allow for very precise measurements of some
of the fundamental constants (such as the fine structure
constant alpha or the Rydberg constant).

We review results published on a method tailored for the formal
evaluation of the atomic energy levels predicted by QED: the
``two-time Green's function method,'' that we present in great detail.
This method allows one to obtain the atomic energy levels predicted by
QED, even when they are degenerate or quasi-degenerate (within the
approximation which considers them as sensitive only to the
electromagnetic field of the nucleus)---this can only be achieved by
one other method, which is very recent. We show that it is possible to
solve fundamental problems raised by the two-time Green's function
method, by providing a (partial) study of the relationship between a
meromorphic function and its perturbative expansion. In order to
enable one to use the two-time Green's function method in practical
calculations of atomic energy levels, we introduce the ``phantom
particle method,'' which allows one to systematically derive an
effective hamiltonian for the levels under study. Finally, we present
a detailed calculation of the ``screened self energy'' contribution to
the effective hamiltonian, which also shows that the phantom particle
method can be applied to the calculation of the energy shift
resulting from any Feynman diagram.

Finally, we extend the most precise numerical method of calculation of
the self energy shift (the most important QED shift), in hydrogen and
hydrogen-like ions. This numerical method allows one to obtain the
self energy shift of any level (it was previously restricted to j <=
3/2). We show that it is possible to obtain the self energy shifts of
numerous levels in hydrogen-like ions with a high level of accuracy.
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Contributor : Eric-Olivier Le Bigot Connect in order to contact the contributor
Submitted on : Thursday, February 2, 2006 - 3:52:37 PM
Last modification on : Thursday, November 18, 2021 - 4:11:27 AM
Long-term archiving on: : Monday, September 20, 2010 - 2:10:40 PM



  • HAL Id : tel-00006418, version 2


Eric-Olivier Le Bigot. QED dans les ions à un et deux électrons : états très excités ou quasi-dégénérés. Physique Atomique [physics.atom-ph]. Université Pierre et Marie Curie - Paris VI, 2001. Français. ⟨tel-00006418v2⟩



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