Abstract
In this paper the slope at q2=0 of the Dirac form factor for the electron vertex in fourth order is calculated. The result is κ2F1(4)q2|q2=0=(απ)2(0.107648). This result affects the energy levels of hydrogenic atoms and can be represented as an addition to the interaction energy density of the electron with the external field in the form ie[Ψ¯(x),γμΨ(x)](2κ2)Aμe(x)×[(α24π2)(0.215296)], where κ is the mass of the electron. This term contributes to the level shift in a hydrogenic atom an energy of δlo[4(zα)4κc2n3](απ)2(0.107648). This calculation reduces the uncertainty in the theoretical result by about 50% to ± 0.1 MHz, which is about the size of the experimental error.