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 ${\mathrm{Th}}^{3+}$ 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 ${}^{232,229}\mathrm{Th}$ and ${}^{229m,229}\mathrm{Th}$. Additionally, we determine the nuclear magnetic dipole and electric quadrupole moments for both the ground and isomeric states of ${}^{229}\mathrm{Th}$ 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 ${}^{229}\mathrm{Th}^{3+}$-based nuclear clocks. 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.

Close

PrevNext

View figure in article

• Electronic structure
• Fine & hyperfine structure
• Isotope shift
• Nuclear radii
• Nuclear shapes and moments
• Stark effect
• Ions
• Electric moment
• Polarizability
• Coupled cluster
• First-principles calculations
• Hartree-Fock methods
• Nonperturbative methods
• Perturbative methods