Finite field calculations of static polarizabilities and hyperpolarizabilities of In$^{+}$ and Sr

TL;DR

This study uses advanced relativistic finite field calculations to determine polarizabilities and hyperpolarizabilities of In$^+$ and Sr, assessing their impact on atomic clock accuracy.

Contribution

It provides detailed relativistic calculations of polarizabilities and hyperpolarizabilities for In$^+$ and Sr, including spin-orbit effects and blackbody radiation shifts.

Findings

Relativistic effects significantly influence polarizability values.

Blackbody radiation shifts are quantified for clock transitions.

Comparison of correlation methods highlights the importance of spin-orbit interaction.

Abstract

The finite field calculations are performed for two heavy frequency-standard candidates In$^+$ and Sr. The progressive hierarchy of electron correlations is implemented by the relativistic coupled-cluster and configuration interaction methods combined with basis set of increasing size. The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities are recommended for the ground state 5s$^2$ $^1S_0$ and low-lying states 5s5p $^3P^{\rm o}_{0,1,2}$ of In$^+$ and Sr. Comparative study of the fully and scalar relativistic electron correlation calculations reveals the effect of the spin-orbit interaction on the dipole polarizabilities of In$^{+}$ and Sr. Finally, the blackbody-radiation shifts due to the dipole polarizability, dipole hyperpolarizability, and quadrupole polarizability are evaluated for the clock transition 5s$^2$ $^1S_0$ - 5s5p $^3P^{\rm o}_0$ of In$^+$ and Sr.