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Aspects of QED in the Framework of Exotic Atoms

Basic principle of Bound-State quantum electrodynamics (BSQED) Status of BSQED in electronic one-electron atoms The fine structure of helium and helium-like ions and the problem of the determination of a Muonic Hydrogen and the proton radius Antiprotonic light-ions

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Aspects of QED in the Framework of Exotic Atoms

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  1. Basic principle of Bound-State quantum electrodynamics (BSQED) Status of BSQED in electronic one-electron atoms The fine structure of helium and helium-like ions and the problem of the determination of a Muonic Hydrogen and the proton radius Antiprotonic light-ions Pionic Hydrogen and pionium Paul Indelicato Laboratoire Kastler Brossel Ecole Normale Supérieure et Université Pierre et Marie Curie Eric-Olivier Le Bigot Stéphane Boucard Philippe Patté,JP Santos,U. Jentschura Aspects of QED in the Framework of Exotic Atoms

  2. History of QED for atoms

  3. Principle of QED • Interaction of electrons with their own radiation field (self-energy) • Two approaches to QED calculations : low Coulomb field or high Coulomb field • Perturbative • Low nuclear charge • Expansion in (Za) • Non perturbative • All nuclei (easier for high Z) • Numerical calculations

  4. A Few Facts for BSQED in Atoms • All-order in (Za) is required even for moderately heavy elements • It is only in 1999 that Accurate All-Order in (Za) Self-Energy calculation have become possible • Vacuum Polarization dominates in Exotic Atoms (makes it easier) • Self-Energy dominates in electronic-Atoms

  5. Quantum Hall effect Solid State Josephson Effect Muonium QED Helium Electron g – 2 h / M(neutron) h / M h / M(Cs) 137,036 990 137,036 000 137,036 010 Value of a as a function of the method

  6. Basic QED contributions • Possibility of particle creation (requires Quantum Field Theory)

  7. Hydrogen Scales

  8. Theory for hydrogen • The most accurate, all order methods are more suitable for high-Z • First calculation (Z=1) of (B) more accurate than experiment was done only in 2000 • Terms of order a2 have been calculated to all orders only for a few heavy elements. • Accuracy on the proton charge radius does not allow to test QED to experimental accuracy Order a Order a2

  9. Theory for two-electron ion • To the difficulties of QED one has to had the slow convergence (1/Z) of correlation corrélations • The exact calculation of A2+B1 in the mid-90’s • Quasi-degenerate states only in 2001 for Z≥18 • A1+A2 slow progress for excited states… • Non-relativistic high accuracy calculation (Hylleraas) still part of the story! 1/Z 1/Z2 1 Order 1/Z compared to 1 electron

  10. A recent history of the fine structure constant a • the best determination of a to date is (CODATA 1998) from the electron magnetic moment measurement of : ge-2=0.001 159 652 188 3(42), [3.7 ppb] which has been calculated from QED by Schwinger (first order term),… and Kinoshita (4th order term): • Other methods: h/mneutron, Josephson effect, Quantum Hall effect, helium fine structure • Distance between the largest and smallest values: 4.9s, Between He fine structure and g-2, 4.2s.

  11. Experimental status of Hydrogen • Experimental precision in the 1s-2s transition (Niering et al. 2000): • 2 466 061 413 187 103(46) Hz (1.810-14) • Rydberg constant measurement [from 2s-nD transitions, de Beauvoir et al (2000)] for comparison with theory: • 109 737.315 685 50(84) cm-1 (7.710-12) • 1S Lamb shift: 8 172.840(22) MHz (2.7 ppm) • Can be improved only if Rydberg constant accuracy is improved

  12. Experimental precision in Hydrogen Lamb shift

  13. Muonic Hydrogen • The ongoing experiment on muonic hydrogen is aiming at a 40ppm measurement of the 2s-2p3/2 splitting, corresponding to 0.11% in the proton radius and 0.008 meV • DE=209.960-5.166r2 meV • Light-by-Light scattering 0.030 (30) meVDisagreement between Pachuki (1996) and Eides et al. (2001) • Nuclear Polarization +0.012 (2) Pachuki (1999), Rosenfelder (2000), Faustov and Marinenko (2000)

  14. QED Contributions to 3d-2p transitions in antiprotonic hydrogen • Vacuum polarization of order (Za) 1.8 eV on 1.7 keV • Vacuum polarization of order a (Za) 15 meV (Kàllén & Sabry A3+C2)+2.2 meV (Loop after Loop C1 to all orders) • Self-energy and mixed diagrams (?) • Relativistic and QED Recoil corrections beyond usual ones need to be investigated

  15. Mixed QED/structure Contributions to 3d-2p transitions in antiprotonic hydrogen • Hyperfine structure (interaction of the antiproton spin and orbital magnetic moment with proton magnetic moment)Antiproton considered as a Dirac Particle • Bohr Weisskopf effect (magnetic moment distribution in the proton) • g - 2 for the antiproton (g = 5.58, not 2!) • As fine and hyperfine structure and g - 2 corrections are of the same order of magnitude we must diagonalize the full hamiltonian to include those effects non-perturbatively • Antiproton and proton size corrections (0.02 meV)

  16. Borie Antiprotonic Hydrogen

  17. Pilkhun Antiprotonic Deuterium

  18. Comparison with Experiment (antiprotonic H)

  19. Comparison with Experiment (antiprotonic D)

  20. Pionic Hydrogen • New experimental effort requires meV accuracy on pionic hydrogen • Very little precision work has been done (pion is a spin 0 boson  cannot use usual QED formalism and codes) • Hyperfine structure correction and recoil corrections need to be investigated.

  21. Status of Pionic Hydrogen QED contributions

  22. High precision QED tests in pionic atoms Accidental coincidence provide ways of very accurate test (~8 meV) of QED calculations in pionic atoms Crystal spectroscopy and exotic atoms, P. Indelicato et L.M. Simons, Quantum Electrodynamics and Physics of the Vacuum, G. Cantatore ed., AIP Conference proceedings, Vol. 564, American Institute of Physics (Melville, New York) pp 152-157, (2001).

  23. Pionium We have evaluated the lowest order two-body (Breit) correction in view of the Dirac experiment Breit Hamiltonian and quantum electrodynamic effects for spinless particles, U.D. Jentschura, G. Soff et P. Indelicato. J. Phys. B: At. Mol. Opt. Phys. 35, 2459-2468 (2002).

  24. New high-resolution, high precision experiments require improved QED calculations to extract strong interaction parameters New tests of QED can be performed in new situations (pionic atoms…) More properties of hadrons must be studied (proton charge radius, magnetic moment distribution of the proton) New developments:exact relativistic pion-electron interactionpionic atoms hyperfine structure More recoil corrections Exact self-energy correction to pionic and muonic atoms Conclusions and perspectives

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