  Predicting the rate for $\mu\to e$ conversion in nuclei for a given set of
effective operators mediating the violation of lepton flavor symmetry crucially
depends on hadronic and nuclear matrix elements. In particular, the
uncertainties inherent in this non-perturbative input limit the discriminating
power that can be achieved among operators by studying different target
isotopes. In order to quantify the associated uncertainties, as a first step,
we go back to nuclear charge densities and propagate the uncertainties from
electron scattering data for a range of isotopes relevant for $\mu\to e$
conversion in nuclei, including $^{40,48}$Ca, $^{48,50}$Ti, and $^{27}$Al. We
provide as central results Fourier-Bessel expansions of the corresponding
charge distributions with complete covariance matrices, accounting for
Coulomb-distortion effects in a self-consistent manner throughout the
calculation. As an application, we evaluate the overlap integrals for $\mu\to
e$ conversion mediated by dipole operators. In combination with modern
ab-initio methods, our results will allow for the evaluation of general $\mu\to
e$ conversion rates with quantified uncertainties.
