Relativistic coupled-cluster theory analysis of energies, hyperfine structure constants, and dipole polarizabilities of Cd${}^{+}$

Abstract

Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd${}^{+}$) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation, second-order many-body perturbation theory and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight importance of various correlation effects in the evaluation of these properties. At the end, we also determine E1 polarizabilities (${\alpha }^{E1}$) of the ground and $5p{}^2{P}_{1/2;3/2}$ states of Cd${}^{+}$ in the {\it ab initio} approach. We estimate them again by replacing some of the E1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high precision experiments of this ion.

arXiv comment10 pages, 7 tables; Accepted in Phys. Rev. A

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• A lower scaling four-component relativistic coupled cluster method based on natural spinors
• Precision determination of the ground-state hyperfine splitting of trapped ${}^{113}$Cd${}^{+}$ ions
• Hyperfine measurement of $6{\text{P}}_{1/2}$ state in ${}^{87}\text{Rb}$ using double resonance on blue and IR transition
• 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
• Determination of hyperfine splittings and Landé $g_J$ factors of $5s{}^2{S}_{1/2}$ and $5p{}^2{P}_{1/2,3/2}$ states of ${}^{111,113}$Cd${}^{+}$ for a microwave frequency standard
• Accurate determination of energy levels, hyperfine structure constants, lifetimes and dipole polarizabilities of triply ionized tin isotopes
• Investigating the $4D_{3/2}|3,\pm 2⟩$--$4D_{5/2}|3,\pm 2⟩$ transition in Nb${}^{4+}$ for a THz atomic clock