  Atomic properties such as field shift constants, magnetic dipole and electric
quadrupole hyperfine structure constants, Land\'e $g_J$ factors, and electric
quadrupole moments that are described by electronic operators with different
ranks and radial behaviors are studied and the role of electron correlation
effects in their determination are investigated. We have adopted the
Dirac-Hartree-Fock method, the second- and third-order relativistic many-body
perturbation theories, and an all-order relativistic many-body method in the
coupled-cluster theory framework considering only the linearized terms and also
all the non-linearized terms in the singles and doubles with partial triples
excitations approximation to carry out these analyses. Variations in the
propagation of electron correlation effects with operators having same angular
factors but different radial behaviors and with different ranks are
highlighted. Corrections from the higher-order relativistic corrections due to
the Breit and quantum electrodynamics interactions to all these properties are
also estimated. Understanding of trends of electron correlation effects in
these properties can be useful to establish accuracies in the theoretical
results of different atomic properties and to substantiate validity of an
approximated many-body method.
