Comprehensive Assessment of $\mathrm{Th}^{3+}$ Properties for Nuclear Clock and Fundamental Physics Applications

TL;DR

This study uses advanced relativistic coupled-cluster calculations to comprehensively evaluate atomic properties of Th$^{3+}$, aiding nuclear clock development and fundamental physics research.

Contribution

It provides highly accurate nuclear charge radii, magnetic moments, and polarizabilities for Th$^{3+}$, incorporating higher-order relativistic effects and excitations for the first time.

Findings

Accurate differential nuclear charge radii for $^{232,229}$Th and $^{229m,229}$Th.

Determination of nuclear magnetic dipole and electric quadrupole moments for Th isotopes.

Significant higher-order relativistic effects influence ground state energies.

Abstract

By employing singles, doubles, and triples excitations within the relativistic coupled-cluster framework, we perform comprehensive calculations of a wide range of atomic properties for the Th$^{3+}$ ion. These properties are essential for advancing nuclear clock technology and probing fundamental physics. Combining our isotope shift parameters with experimental data, we estimate highly accurate values of the differential nuclear charge radii for $^{232,229}$Th and $^{229m,229}$Th. Additionally, we determine the nuclear magnetic dipole and electric quadrupole moments for both the ground and isomeric states of $^{229}$Th by combining measured hyperfine structure constants with our theoretical calculations. Our precise evaluations of electric dipole polarizabilities and hyperfine-induced quadrupole moments are critical for assessing systematic uncertainties in $^{229}$Th$^{3+}$-based nuclear clock. Notably, we observe unexpectedly significant contributions from higher-order relativistic effects and excitations involving orbitals with higher angular momentum, which markedly influence the energies of the ground state and its fine-structure partner. These results highlight the substantial challenges in achieving highly accurate predictions for these properties.