Vacuum polarization in a strong Coulomb field. I. Induced point charge

This is the first of a series of three papers concerned with the short-distance behavior of the vacuum polarization potential. It is this region that gives the principal energy level shift in heavy muonic atoms. In this paper we compute the induced vacuum polarization point charge that appears in the limit of a point nuclear charge source. Our result, computed analytically to all orders of $Z\alpha$, agrees with an earlier calculation of Wichmann and Kroll. We have been able to simplify the calculation considerably by taking advantage of a zero-electron-mass limit and by using formal operator and determinantal techniques.