Vacuum Polarization in High-Z, Finite-Size Nuclei

Abstract

We have calculated vacuum-polarization charge densities to all orders ${\left(Z\alpha \right)}^n\alpha$ for realistic nuclei of finite extent. In muonic Pb, orders $n>~3$ contribute -34 ± 2 eV to the $5g\to 4f$ transitions, compared with the point nucleus value of -50 eV. This increases the discrepancy (first reported by Dixit et al.) to $E\left(\mathrm{theor}\right)-E\left(\mathrm{expt}\right)=57\mathrm{}\pm 18 \mathrm{eV} (5\mathrm{}{g}_{\frac{9}{2}}\to 4f_{\frac{7}{2}}) \mathrm{and} 72\pm 21 \mathrm{eV} (5\mathrm{}{g}_{\frac{7}{2}}\to 4f_{\frac{5}{2}})$. Contributions to low-lying states show nearly an order-of magnitude reduction.