  Background: The nuclear charge radius and distribution are the most
fundamental quantities of the atomic nucleus. From the muonic transition
energies, the absolute charge radius has been experimentally obtained, while
there have been no established methods to discuss the distribution.
  Purpose: The muonic transition energies for five palladium isotopes with the
mass number $A = 104$, $105$, $106$, $108$ and $110$ were measured. The
procedure to deduce the charge radii and the method to discuss the charge
distribution from the muonic transition energies are proposed.
  Method: The experiment was performed at the MuSIC-M1 beamline at Research
Center for Nuclear Physics, Osaka University. A continuous muon beam impinged
on the enriched palladium targets. Muonic X rays were measured by high-purity
germanium detectors.
  Results: The muonic transition energies up to $4f$-$3d$ transitions were
determined for five palladium isotopes.
  Discussion and conclusion: The root-mean-square charge radii are deduced
assuming the two-parameter Fermi distribution. The charge distribution of the
nucleus is discussed employing the Barrett model. The muonic transition
energies of the $3d$-$2p$ transitions are crucial to discuss both the charge
radius and the charge distribution.
