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All-Order Wichmann and Kroll Contribution in Heavy Electronic and Exotic Atoms

We present a theoretical study of the Wichmann and Kroll correction to the one-loop vacuum polarization (VP) to all-orders in $αZ$. We consider electronic, muonic, and antiprotonic atoms for a wide range of nuclear charge numbers and explicitly investigate the influence of finite nuclear size effects and different nuclear models. Moreover, we place special emphasis on circular Rydberg states in the exotic atoms as they have recently attracted interest as a tool to perform isolated tests of strong-field QED. We find that the higher-order vacuum polarization is strongly enhanced in exotic atoms and remains large enough in highly excited Rydberg states that an accurate treatment is crucial for the analysis of upcoming spectroscopy experiments like PAX. Moreover, our calculations show that the VP contribution to the Lamb shift in these exotic Rydberg states has almost no dependence on the structure of the nucleus.