Relativistic coupled-cluster theory analysis of unusually large correlation effects in the determination of $g_j$ factors in Ca${}^{+}$

Abstract

We investigate roles of electron correlation effects in the determination of the $g_j$ factors of the $4s{}^2{S}_{1/2}$, $4p{}^2{P}_{1/2}$, $4p{}^2{P}_{3/2}$, $3d{}^2{D}_{3/2}$, and $3d{}^2{D}_{5/2}$ states, representing to different parities and angular momenta, of the Ca${}^{+}$ ion. Correlation contributions are highlighted with respect to the mean-field values evaluated using the Dirac-Hartree-Fock method, relativistic second order many-body theory, and relativistic coupled-cluster (RCC) theory with the singles and doubles approximation considering only the linear terms and also accounting for all the non-linear terms. This shows that it is difficult to achieve reasonably accurate results employing an approximated perturbative approach. We also find that contributions through the non-linear terms and higher-level excitations such as triple excitations, estimated perturbatively in the RCC method, are found to be crucial to attain precise values of the $g_j$ factors in the considered states of Ca${}^{+}$ ion.

arXiv comment10 pages, 2 figures and 4 tables

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Cited by in corpus (2)

• Diverse Trends of Electron Correlation Effects for Properties with Different Radial and Angular Factors in an Atomic System: A case study in Ca${}^{+}$
• Roles of electron correlation effects for accurate determination of $g_j$ factors of low-lying states of ${}^{113}$Cd${}^{+}$ and their applications to atomic clock