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Recoil effects in the hyperfine structure of QED bound states

G. T. Bodwin, D. R. Yennie, and M. A. Gregorio

G. T. Bodwin

  • High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439

D. R. Yennie

  • Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853

M. A. Gregorio

  • Instituto de Fisica, Universidade Federal de Rio de Janeiro, Rio de Janeiro, Brazil

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Rev. Mod. Phys. 57, 723 – Published 1 July, 1985

DOI: https://doi.org/10.1103/RevModPhys.57.723

Abstract

The authors give a general discussion of the derivation from field theory of a formalism for the perturbative solution of the relativistic two-body problem. The lowest-order expression for the four-point function is given in terms of a two-particle three-dimensional propagator in a static potential. It is obtained by fixing the loop energy in the four-dimensional formalism at a point which is independent of the loop momentum and is symmetric in the two particle variables. This method avoids awkward positive- and negative-energy projectors, with their attendant energy square roots, and allows one to recover the Dirac equation straightforwardly in the nonrecoil limit. The perturbations appear as a variety of four-dimensional kernels which are rearranged and regrouped into convenient sets. In particular, they are transformed from the Coulomb to the Feynman gauge, which greatly simplifies the expressions that must be evaluated. Although the approach is particularly convenient for the precision analysis of QED bound states, it is not limited to such applications. The authors use it to give the first unified treatment of all presently known recoil corrections to the muonium hyperfine structure and also to verify the corresponding contributions through order α2lnαEF in positronium. The required integrals are evaluated analytically.

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Rev. Mod. Phys. 57, 723– Published 1 July, 1985

    © 1985 American Physical Society

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