Nuclear-Size Effects on Vacuum Polarization in Muonic Pb

Abstract

The effect of finite nuclear size on the vacuum-polarization charge density is studied. The results to third order $\alpha {\left(Z\alpha \right)}^3$, and to all orders $\alpha {\left(Z\alpha \right)}^n$, $n>~3$, are presented with special attention focused on the $5g_{\frac{9}{2}}-4f_{\frac{7}{2}}$ transition in muonic Pb. In addition, the accuracy of analytic calculations exploiting the smallness of the electron mass and of the nuclear radius is discussed.