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Title: Laser-dressed vacuum polarization in a Coulomb field

Abstract

We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a ''polarized Lamb shift.'' In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like 1/r{sup 3} at large distances, unlike the Uehling potential, which vanishes exponentially for large r. The energy corrections are of the same order of magnitude for hydrogenic levels, irrespective of the angular momentum quantum number. The induced current leads to a transition dipole moment which oscillates at the second harmonic of the laser frequency and is mediated by second-ordermore » harmonic generation in the vacuum-polarization loop. In the far field, at distances r>>1/{omega} from the nucleus ({omega} is the laser frequency), the laser induces mutually perpendicular electric and magnetic fields, which give rise to an energy flux that corresponds to photon fusion leading to the generation of real photons, again at the second harmonic of the laser. Our investigation might be useful for other situations where quantum field theoretic phenomena are subjected to external fields of a rather involved structure.« less

Authors:
; ; ;  [1];  [2]
  1. Budker Institute of Nuclear Physics, 630090 Novosibirsk (Russian Federation)
  2. (Germany)
Publication Date:
OSTI Identifier:
20786440
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052104; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; CHARGE DENSITY; COULOMB FIELD; CURRENT DENSITY; DIPOLE MOMENTS; ELECTROMAGNETIC FIELDS; HARMONIC GENERATION; LAMB SHIFT; LASER RADIATION; MAGNETIC FIELDS; PERTURBATION THEORY; PHOTON-ATOM COLLISIONS; PHOTONS; POTENTIALS; QUADRUPOLE MOMENTS; QUANTUM ELECTRODYNAMICS; RADIATIVE CORRECTIONS; ROTATIONAL STATES; SYMMETRY; TIME DEPENDENCE; VACUUM POLARIZATION

Citation Formats

Milstein, A. I., Terekhov, I. S., Jentschura, U. D., Keitel, C. H., and Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg. Laser-dressed vacuum polarization in a Coulomb field. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Milstein, A. I., Terekhov, I. S., Jentschura, U. D., Keitel, C. H., & Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg. Laser-dressed vacuum polarization in a Coulomb field. United States. doi:10.1103/PHYSREVA.72.0.
Milstein, A. I., Terekhov, I. S., Jentschura, U. D., Keitel, C. H., and Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg. Tue . "Laser-dressed vacuum polarization in a Coulomb field". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786440,
title = {Laser-dressed vacuum polarization in a Coulomb field},
author = {Milstein, A. I. and Terekhov, I. S. and Jentschura, U. D. and Keitel, C. H. and Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg},
abstractNote = {We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a ''polarized Lamb shift.'' In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like 1/r{sup 3} at large distances, unlike the Uehling potential, which vanishes exponentially for large r. The energy corrections are of the same order of magnitude for hydrogenic levels, irrespective of the angular momentum quantum number. The induced current leads to a transition dipole moment which oscillates at the second harmonic of the laser frequency and is mediated by second-order harmonic generation in the vacuum-polarization loop. In the far field, at distances r>>1/{omega} from the nucleus ({omega} is the laser frequency), the laser induces mutually perpendicular electric and magnetic fields, which give rise to an energy flux that corresponds to photon fusion leading to the generation of real photons, again at the second harmonic of the laser. Our investigation might be useful for other situations where quantum field theoretic phenomena are subjected to external fields of a rather involved structure.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • We continue our study of the behavior of the vacuum polarization near the nucleus, the region of importance for heavy muonic atoms. We show that the vacuum polarization potential induced by a point nuclear charge can be expanded in certain integral and nonintegral powers of the radius r, and expansion involving r$sup -1$, r, r , and higher terms. The coefficient of the r -1 term was computed in the previous paper, analytically, to all orders of Zα. In this paper, we compute the coefficients of the r and r$sup 2 terms analytically, to all orders in Zα. Ourmore » results agree in third order with earlier calculations, which had been done only to this order. Parts of our calculation are considerably simplified by an expansion in powers of the electron mass using formal operator and determinantal techniques.« less
  • This is the first of a series of three papers concerned with the short- distance behavior of the vacuum polarization potential. It is this region that gives the principal energy level shift in heavy muonic atoms. In this paper, we compute the induced vacuum polarization point charge that appears in the limit of a point nuclear charge source. Our result, computed analytically to all orders of Z$alpha$, agrees with an earlier calculation of Wichmann and Kroll. We have been able to simplify the calculation considerably by taking advantage of a zero- electron-mass limit and by using formal operator and determinantalmore » techniques.« less
  • We compute the change in the vacuum polarization near a high-Z nucleus arising from the finite extent of the nuclear charge density. A massless- electron technique is exploited to permit an analytical calculation of the effect to all orders in Z$alpha$. Applications to muonic atoms are of particular interest as tests of quantum electrodynamics. The calculation of muonic energy level shifts is carried out to lowest order in the ratio of the nuclear radius to the radius of the muonic orbit. This approximation is appropriate to many muonic states with large orbits. Our analytical results are in excellent agreement withmore » numerical studies by Gyulassy and give as a special case the order $alpha$ (Z$alpha$)$sup 3$ calculation of Arafune. The effect on muonic x rays such as those produced in the 5g$sub 9$/$sub 2$ $Yields$ 4f$sub 7$/$sub 2$ transition in $sup 208$Pb is about 5 eV, increasing slightly the discrepancy between theory and experiment in such systems.« less