Finite-nuclear-size corrections to the Uehling potential

A study is made of finite-nuclear-size corrections to the Uehling potential for the ground state of hydrogenlike atoms (Z=1 and 80). The exact relativistic correction is compared to the results of perturbation theory and to nonrelativistic results based upon the approximations of Zemach. Perturbation theory and the nonrelativistic approximation are consistent with the exact calculation at Z=1, but not at Z=80. In the nonrelativistic approximation, this size correction is (1/2)α(Zα${)}^5$(R/${\mathrm{hlambda}}_e$ ${)}^2$mc ${}_{}{}^2{}_{}{}^{}$, where R is the rms radius of the nucleus.