Skeleton Integral Approach to Calculations of Radiative Corrections

1 Skeleton Integral Approach to Calculations of Radiative Corrections 

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. 

The magnitude of the correction of order a Za) may be easily estimated before the calculation is carried out. We need to take into account the skeleton factor 4m Za) /n discussed above in Sect. 2.3, and multiply it by an extra factor a Za). Naively, one could expect a somewhat smaller factor a.(Za)j%. However, it is well known that a convergent diagram with two external photons always produces an extra factor tt in the numerator, thus compensating the factor TT in the denominator generated by the radiative correction. Hence, calculation of the correction of order a(Za) should lead to a numerical factor of order unity multiplied by 4ma(Za) /n . 

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