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

TL;DR

This paper employs relativistic coupled-cluster theory to analyze electron correlation effects on energies, hyperfine constants, and polarizabilities of Cd$^+$, providing detailed insights and improved estimates for high-precision applications.

Contribution

It presents a comprehensive relativistic coupled-cluster analysis of Cd$^+$ properties, including correlation effects and refined polarizability estimates for the first time.

Findings

Correlation effects significantly influence energy and hyperfine constants.

Important RCC terms highlight the role of various electron correlations.

Refined E1 polarizability values aid high-precision experiments.

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 $5p \ ^2P_{1/2;3/2}$ 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.