Radiative corrections, higher-order

Radiative Corrections of Order Q. Zcxym and of Higher Orders... 

Leading recoil corrections in Za (of order (Za) (m/M)") still may be taken into account with the help of the effective Dirac equation in the external field since these corrections are induced by the one-photon exchange. This is impossible for the higher order recoil terms which reflect the truly relativistic two-body nature of the bound state problem. Technically, respective contributions are induced by the Bethe-Salpeter kernels with at least two-photon exchanges and the whole machinery of relativistic QFT is necessary for their calculation. Calculation of the recoil corrections is simplified by the absence of ultraviolet divergences, connected with the purely radiative loops. 

We have seen above that calculation of the corrections of order a"(Za) m (n > 1) reduces to calculation of higher order corrections to the properties of a free electron and to the photon propagator, namely to calculation of the slope of the electron Dirac form factor and anomalous magnetic moment, and to calculation of the leading term in the low-frequency expansion of the polarization operator. Hence, these contributions to the Lamb shift are independent of any features of the bound state. A nontrivial interplay between radiative corrections and binding effects arises first in calculation of contributions of order a Za) m, and in calculations of higher order terms in the combined expansion over a and Za. 

Calculation of the state-dependent nonlogarithmic contribution of order a(Za) is a difficult task, and has not been done for an arbitrary principal quantum number n. The first estimate of this contribution was made in [63]. Next the problem was attacked from a different angle [64, 65]. Instead of calculating corrections of order a(Za) an exact numerical calculation of all contributions with one radiative photon, without expansion over Za, was performed for comparatively large values of Z (n = 2), and then the result was extrapolated to Z = 1. In this way an estimate of the sum of the contribution of order a(Za) and higher order contributions a(Za) was obtained (for n = 2 and Z = 1). We will postpone discussion of the results obtained in this... 

Higher Order Radiative Corrections to the Finite Size Effect... 

One can consider also higher order radiative corrections to the finite size effect. Such contribution originating from very small distances and enhanced by the large logarithm ln(l/(mro)) (ro here is the radius of the nucleus) was obtained in [50, 51, 55]. Its relative magnitude with respect to the leading finite size contribution is a Za) and it is universal for S and P state. 

Higher order in mass ratio radiative-recoil corrections of order a Za) m/M) Ep, n > 2, are generated by the same set of diagrams in Fig. 10.5, in Fig. 10.6 and in Fig. 10.7 with the radiative insertions in the electron and muon lines, and with the polarization insertions in the photon lines, as the respective corrections of the previous order in the mass ratio. Analytic calculation of the correction of order a Za) m/M) Ep in [52] proceeds as in that case, the only difference is that now one has to preserve all contributions which are of second order in the small mass ratio. It turns out that all such corrections are generated at the scale of the electron mass, and one obtains for the sum of all corrections [52]... 

Abstract. We review our recent results on higher order corrections in positronium physics. We discuss a calculation of the recoil 0(ma6) corrections to the hyperfine splitting [1] and energy levels of a positronium atom [2], 0(ma7 In2 a) contributions to the positronium S-wave energy levels [3] and Ola2) radiative corrections to the parapositronium decay rate [4],... 

There are several quantities in positronium physics where higher order radiative corrections have to be taken into account for the theoretical prediction to match the experimental precision. For the hyperfine splitting of the ground state, Av = E(13Si) — Eil1 So), the two best experimental values are [5,6]... 

Predictions of the values of and 34 from standard theory - dominantly the QED terms - requires values for many atomic constants including m, and Av as well as the calculation of higher order QED radiative corrections. The... 

Higher-Order Radiative Corrections Corrections from diagrams with two virtual photons are given by... 

Self energy and vacuum polarization of order a and the nuclear size account for the measured Lamb shift in hydrogenlike heavy ions at the current level of accuracy. Radiative corrections of the order contribute to the Lamb shift of the lsi/2 state and amount to about 1 eV for uranium. Facing higher precision in experiments, these corrections have to be evaluated to yield a reliable Lamb shift calculation. 

Higher order terms in the perturbation series lead to more complex expressions which have been analyzed in detail, in particular for highly ionized atoms. Terms appear which reproduce the expressions of nonrelativistic many-body perturbation theory (MBPT) [66,70,71] together with further radiative corrections. Generally speaking, radiative correction terms, even in second order, include contributions from positron states. Apart from hinting how such higher order terms can be included in the theory, we shall not need to discuss them in this chapter. 

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