Recalculation of the Crossed-Graph Contribution to the Fourth-Order Lamb Shift

This paper reports an analytic calculation of the "crossed"-graph contribution to the fourth-order radiative correction of the slope of the Dirac form factor of the free-electron vertex at zero momentum transfer. The result, $m^2{F}_1^{\prime }\mathrm{}\left(0\right)=\frac{{\alpha }^2}{{\pi }^2}[-\frac{13}{36}\ln {\lambda }^{-2\mathrm{}}+\frac{411}{864}{\pi }^2+\frac{7}{12}{\pi }^2\ln 2+\frac{313}{8}\zeta \mathrm{}(3)-\frac{92189}{1728}]=\frac{{\alpha }^2}{{\pi }^2}(-\frac{13}{36}\ln {\lambda }^{-2\mathrm{}}+2.3659)$ [where $\zeta \mathrm{}\left(3\right)\mathrm{}$ is the Riemann $\zeta$ function of argument 3], confirms the result of Appelquist and Brodsky.