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The extractions of nuclear charge radii from muonic atom spectroscopy for$^{40}$Ca and $^{208}$Pb are revisited to analyze the model dependenciesinduced by employing a Fermi-type charge distribution. For that, the chargedensities, together with the corresponding muonic transition energies,calculated by the covariant density functional theory are used as a benchmark.The root-mean-square deviation of transition energies is calculated toquantitatively investigate the sensitivities of transition energies to thedetails of the two-parameter Fermi distribution. It is found that the secondand fourth moments of the charge distribution can be extracted accurately fromthe muonic atom spectroscopy without much model dependencies, whereas theobtained two-parameter Fermi distributions cannot reproduce the details of thebenchmarking charge densities and, in particular, its surface-diffusenessparameter cannot be determined accurately with the present experimentaluncertainties on the muonic transition energies.

Revisiting the extraction of charge radii of $^{40}$Ca and $^{208}$Pb with muonic atom spectroscopy