/- ' ' - ' ·: '. ·'-• ·. ' To be .p~b1i$h~d: in 1 '#iavyion Atomic-· -LBL-6087 , c.\ Physics,!'lva'f:lA; Sellip,, ed., (/\ SLAC-PUB-1889 :Spri11ger-Ve:rlag;' (19.77) .·· ·.-.: >;: -. ;·-:. QUANTUM'ELECTRODYNAMICS iN STRON6 AND SUPERCRITICAL FIELDS "- . -: ' -, ~ for Reference ·Stanley J~ Brodsky ..an,d Peter J. Mohr Not to be taken from this room Febxuary 19 77 ·, · ... Prepared for the u: .S.· :E:;ne:rgy Resear.ch and. Developrnent Administration' )..lnd~;r:~c ont:ract w;. 7 40 5-ENG ... 48 • • • • - ~-- • • ~ • • • < • ,,- • - • ' • - • - •• )•' DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. 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The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Govemment or any agency thereof or the Regents of the University of California. 0 LBL-6087 SLAC-PUB-1889 QUANTUM ELECTRODYNAMICS IN STRONG AND SUPERCRITICAL FIELDS Stanley J. Brodsky Stanford Linear Accelerator Center ... ... Stanford University Stanford, California 94305 Peter J. Mohr Department of Physics and Lawrence Berkeley Laboratory University of California Berkeley, California 94720 February 1977 ,, TABLE OF C0.\7E~~S Introduction . A.l The Electrod)~amics of High-Z Electronic Atoms 4 A.l.l Lamb Shift in Hydrogenlike Ions 4 A.l. 2 Lamb Shift in Heliumlike Ions 9 A.l. 3 Quantt.nn Electrodynamics in High-Z .'leutral Atoms 11 A.l.4 High-Z Atoms and Limits on Nonlinear Modifications of QED .................... 14 A.l.S Wichmann-Kroll Approach to Strong-Field Electrodynamics 15 A. 2 The Electrodynamics of High-Z Muonic Atoms· 21 A.2.1 General Features 21 A.2.2 Vacut.nn Polarization 24 A.2.3 Additional Radiative Corrections 32 A.2.4 Nuclear Effects 34 A.2.5 Electron Screening 35 A. 2.6 Summary and. Comparison with Experiment 37 A.2.7 Muonic Helium 41 A.2.8 Nonperturbative Vacuum Polarization Modification and Possible Scalar Particles . • . 45 A. 3 Quantum Electrodynamics in Heavy-Ion Collisions and Supercritical Fields . • . 48 A.3.1 Electrodynamics for Za > 1 48 A.3.2 Spontaneous Pair Production in Heavy-Ion Collisions 55 A.3.3 Calculation of the Critical Internuclear Distance 61 A. 3.4 Calculation of the Spontaneous Positron Production Rate 62 A.3.5 Induced Versus Adiabatic Pair Production 69 A.3.6 Vacancy Formation in Heavy-Ion Collisions 72 A.3.7 Nuclear Excitation and Other Background Effects 73 A.3.8 Radiative Corrections in Critical Fields . 75 A.3.9 Coherent Production of Photons in Heavy-Ion Collisions 77 ·A.3.10 Self-Neutralization of Matter 78 A.3.11 Very Strong ~~gnetic Field Effects 79 0 Conclusion ... 81 Acknowledgments 83 References . 84 Figure capt ions 95 Figures 99 -2- heavy-ion collision. Somewhat complementary to these tests are the studies of Delbri.ick scattering (elastic scattering of photons by a strong Coulomb I NTROWCf I a-< field) reviewed in Ref. A.2. Quantum electrodynmnics (QED), the theory of the interactions of One of the intriguing aspects of high field strength quantum electro­ electrons and nruons via photons, has now been tested both to high precision d~Jmnics is the possibility that it .may provide a model for quark dynmnics. - at the ppm level - and to short distances of order 10 ·l4 - 10 ·lS em. Present theoretical ideas for the origin of the strong interactions have The short distance tests, particularly the colliding beam measurements of focused on renorrnalizable field theories, such as quantum chromodynmnics + - + - + - e e + ~ ~, yy, and e e. [A.l], are essentially tests of QED in the Bo1n (QCD), where.the quarks are the analogues of the leptons, and the gluons approximation. On the other hand, the precision anomalous. magnetic moment the generalizations of the photon - are themselves charged (non-abelian • and-atomic physics measurements check the higher order loop corrections and Yang-Mills theory). In contrast to QED where the vacuum polarization predictions dependent on the renormalization procedure. Despite the strengthens the charged particle interaction at short distances, in QCD extraordinary successes, it is still important to investigate the validity the interactions weaken at short distances, and (presumably) become very of QED in the strong field domain. In particular, high-Za atomic physics strong at large separations. tests, especially the Lamb shift in high-Z hydrogenic atoms, test the QED To see the radical possibilities in strong fields, suppose a is large amplitude in the situation where the fermion propagator is far off the mass in QED and the first bound state of positroniwn has binding energy e > m. shell and cannot be handled in perturb~tion theory in Za, but where The total mass of the atom 71t is then less than the mass of a free electron the renormalization progrmn for perturbation theory in a must be used. 711 = 2m - e < m. Consider then an experiment in which an e + e · pair is High-Z heavy--ion. collisions can be used to probe the Dirac spectrum in produced near threshold- e.g. via a weak.current process .. -Since an the non-perturbative domain of high Za, where spontaneous positron production additional virtual pair may be present, the produced pair can spontaneously can occur, and where two different vacuum states must be considered. decay to two positronium atoms in .the ground state, each with finite kinetic Another reason to pursue the high-·Za domain is that the spectrum of energy. Thus bound states; and not free fermions, are produced! It is radiation. emitted when two colliding h~avy ions (temporarily) unite can lead clearly an interesting question.whether strong field strength in QED can to a better understanding·of relativistic molecular physics. This physics provide a mechanism analogous to quark confinement in hadron dynmnics. is reviewed .in the accompanying articl~s of this volume. Furthermore, the The work 'of K. WILSON [A. 3] and J. MANOOLA [A-4'] is especially relevant atomic spectra of the low-lying electron states and outgoing positron here .. The studies of spontaneous pair production in heavy-ion collisions continua reflect the nature of the nuclear. charge distribution, and could ,~ .. ..:: .. (see Section A.3) provide a simple phenomenological-framework where some be a useful. tool in unraveling the nuclear physics and dynamics of a close 0 of the effects of strong fields can be tested. -4- It should be noted that our review only touches a limited aspect of A.l THE ELECTRODYNAMICS OF HIGH-Z ELECTRONIC ATOMS high-Za electrodynamics. We consider only the cases of a fixed or heavy A.l.l Lamb Shift in Hydrogenlike Ions source for a high-Za Coulomb potential. An important open question concerns the behavior of the Bethe-Salpeter equation for positronium in the large a At present the most precise and sensitive way to test quantum electro- domain, and in particular, whether the binding energy can become comparable dynamics at high field strength is to compare the theory and measurements to the mass of the constituents so that 7TL = 2m- e ~ 0. of the classic Lamb shift interval, the 2SL - 2P .. separation in hydrogen! ike . ~ ~ The organization of this artiCle is as follows: . We review in detail ions. In recent work on the Lamb shift, measurements have been extended to the recent work on the atomic spectra of high-Z electronic (Section A.l) hydrogenlike argon (Z = 18) by an experiment at the Berkeley SuperHILAC [A. 5). and muonic atoms (Section A.2), including muonic helium, with emphasis on As we shall see, such experiments provide an important test of QED in strong • the Lamb shift and vacuum polarization corrections wh'ich test strong field fields .. The higher order binding terms in the theory which are small in quantum electrodynamics. The theoretical framework of the QED calculations hydrogen become relatively more important at high Z. For example, the terms for strongfields is discussed in Section A.l.5. The. constraints on non­ of order a(Za) 6 which contribute 0.016% of the Lamb shift in hydrogen give perturbative vacuum polarization modifications and possible scalar particles 12% of the Lamb shift in hydrogenlike argon. The theoretical contributions are presented in.Section A.2.8. · A review of recent work on the quantum to the Lamb shift are by now well established [A.6,7]. Our purpose here electrodynamics of heavy-ion collisions, particularly the dynamics of will be to summarize these contributions as an aid to testing the validity ,-.l~· ' .. positron production, is presented in Section A.3. In addition to reviewing of the theory. the phenomenology and calculational methods (Sections A.-3. 2 - A. 3. 4), we also The dominant part of the Lamb shift is given by the self-energy and .-.!_ discuss the parameters for possible experiments, with a brief review of vacuum polarization of order a, corresponding to the Feynman diagrams in vacancy formation (Section A.3.6) and background. effects (Section A.3.7). Fig. A.l(a) and (b). In the past, most of the theoretical work on the self­ In our review of heavy-ion collisions we will also touch on several new .