Vacuum Polarization in Mesonic Atoms

Abstract

The effects of vacuum polarization on the energy levels of $\ensuremath{\pi}$ and $\ensuremath{\mu}$ mesonic atoms are computed to the lowest order for states $1s(Z<~12)$, $2p(Z<~30)$, $3d(Z<~82)$, $4f(Z<~82)$. If one ignores the finite size of the nucleus, these results may be written explicitly in a closed form. The effect of the finite size of the nucleus is estimated and shown to be 8 percent for all states considered. Since the virtual pairs are described here by plane waves, the fractional error in these results is of order ${(Z\ensuremath{\alpha})}^{2}$.