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Muonic atom transitions have been measured for almost all stable nuclei toextract nuclear structure properties, including nuclear charge radii andquadrupole moment. To investigate the possibilities of extracting higher-orderradial moments of nuclear charge density %what kind of information of nuclearcharge distribution can be extracted precisely from muonic atom spectroscopy, atheory-to-theory benchmark analysis based on a model-independent densitydistribution, i.e., the Fourier-Bessel series expansion instead oftwo-parameter Fermi distribution, is performed by taking $^{208}$Pb as anexample, where nuclear charge density obtained from the relativistic continuumHartree-Bogoliubov calculation is used as the benchmark. It is found that theextractions of the higher-order moments, i.e., the fourth and sixth moments inaddition to the second moment are feasible with high accuracy. Moreover, thecharge form factor in the low-$q$ region can also be well extracted.

The extraction of higher-order radial moments of nuclear charge density from muonic atom spectroscopy