Finite-field calculation of the polarizabilities and hyperpolarizabilities of Al${}^{+}$

Abstract

In this study, accurate static dipole polarizability and hyperpolarizability are calculated for Al${}^{+}$ ground state 3s${}^2$ ${}^1$S${}_0$ and excited state $3s3p$ ${}^3$P${}_J$ with $J$=0, 1, 2. The finite-field computations use energies obtained with the relativistic configuration interaction approach and the relativistic coupled-cluster approach. Excellent agreement with previously recommended values is found for the dipole polarizability of Al${}^{+}$ ground state 3s${}^2$ ${}^1$S${}_0$ and excited state $3s3p$ ${}^3$P${}_0$ as well as the hyperpolarizability of the ground state 3s${}^2$ ${}^1$S${}_0$. The recommended values of the dipole polarizability of the Al${}^{+}$ $3s3p$ ${}^3$P${}_1$ and ${}^3$P${}_2$ and the hyperpolarizability of Al${}^{+}$ $3s3p$ ${}^3$P${}_0$, ${}^3$P${}_1$, and ${}^3$P${}_2$ are also given. The impacts of the relativity and spin-orbit coupling are elucidated by analyzing the angular momentum dependence of the dipole polarizability and the hyperpolarizability and comparing the fully and scalar relativistic calculated data. It is shown that the impact of the relativity and spin-orbit coupling are small for the dipole polarizability but become significant for the hyperpolarizability. Finally, the black-body radiation shifts contributed by the dipole polarizability and hyperpolarizability respectively are evaluated for transitions of Al${}^{+}$ 3s${}^2$ ${}^1$S${}_0$ to $3s3p$ ${}^3$P${}_J$ with $J$=0, 1, 2.

15pages,3 tables

References in corpus (4)

• Multipolar theory of black-body radiation shift of atomic energy levels and its implications for optical lattice clocks
• Tune-out wavelengths for the alkaline earth atoms
• Ba${}^{+}$ Quadrupole Polarizabilities: Theory versus Experiment
• Black-body radiation shift of the Ga${}^{+}$ clock transition

Cited by in corpus (3)

• Electric dipole polarizability of group-IIIA ions using PRCC: Large correlation effects from nonlinear terms
• Finite field calculations of static polarizabilities and hyperpolarizabilities of In${}^{+}$ and Sr
• A scheme for quantum-logic based transfer of accuracy in polarizability measurement for trapped ions using a moving optical lattice