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Background: The nuclear charge radius and distribution are the mostfundamental quantities of the atomic nucleus. From the muonic transitionenergies, the absolute charge radius has been experimentally obtained, whilethere have been no established methods to discuss the distribution.  Purpose: The muonic transition energies for five palladium isotopes with themass number $A = 104$, $105$, $106$, $108$ and $110$ were measured. Theprocedure to deduce the charge radii and the method to discuss the chargedistribution from the muonic transition energies are proposed.  Method: The experiment was performed at the MuSIC-M1 beamline at ResearchCenter for Nuclear Physics, Osaka University. A continuous muon beam impingedon the enriched palladium targets. Muonic X rays were measured by high-puritygermanium detectors.  Results: The muonic transition energies up to $4f$-$3d$ transitions weredetermined for five palladium isotopes.  Discussion and conclusion: The root-mean-square charge radii are deducedassuming the two-parameter Fermi distribution. The charge distribution of thenucleus is discussed employing the Barrett model. The muonic transitionenergies of the $3d$-$2p$ transitions are crucial to discuss both the chargeradius and the charge distribution.

Muonic X-Ray Measurement for the Nuclear Charge Distribution: the Case of Stable Palladium Isotopes