Vacuum-polarization correction in muonic molecules

The vacuum-polarization correction (given by the expectation value of the Uehling potential) to the energies of the S states of muonic molecules is calculated using very accurate wave functions. The present results indicate that the values accepted so far in the literature for this correction had been underestimated by a factor of 2--8 (depending on the state of interest) due to insufficient quality of the wave functions used. Expectation values of the interparticle distances, the distances squared, and the inverses of the distances are presented.