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Atomic properties such as field shift constants, magnetic dipole and electricquadrupole hyperfine structure constants, Land\'e $g_J$ factors, and electricquadrupole moments that are described by electronic operators with differentranks and radial behaviors are studied and the role of electron correlationeffects in their determination are investigated. We have adopted theDirac-Hartree-Fock method, the second- and third-order relativistic many-bodyperturbation theories, and an all-order relativistic many-body method in thecoupled-cluster theory framework considering only the linearized terms and alsoall the non-linearized terms in the singles and doubles with partial triplesexcitations approximation to carry out these analyses. Variations in thepropagation of electron correlation effects with operators having same angularfactors but different radial behaviors and with different ranks arehighlighted. Corrections from the higher-order relativistic corrections due tothe Breit and quantum electrodynamics interactions to all these properties arealso estimated. Understanding of trends of electron correlation effects inthese properties can be useful to establish accuracies in the theoreticalresults of different atomic properties and to substantiate validity of anapproximated many-body method.

journal of physics. b, atomic molecular and optical physics/journal of physics. b, atomic, molecular and optical physics

Diverse Trends of Electron Correlation Effects for Properties with  Different Radial and Angular Factors in an Atomic System: A case study in  Ca$^{+}$