Hyperfine-structure constants of the ${}^{45}$Sc II ion and the nuclear quadrupole moment

Abstract

In this work, we calculate the hyperfine-structure constants of the ${}^{45}$Sc${}^{+}$ ion using a relativistic hybrid approach that combines configuration-interaction and coupled-cluster singles-and-doubles methods. Magnetic-dipole and electric-quadrupole hyperfine-structure constants are determined for the states arising from the $3d4s$, $3d^2$, $4s^2$, $4s4p$, $3d4p$, $3d5s$, $3d4d$, and $3d5p$ configurations. For most of these states, our magnetic-dipole hyperfine-structure constants agree well with available experimental data and represent a substantial improvement over previous theoretical results. By combining our calculated electric-field gradients with the measured electric-quadrupole hyperfine-structure constants for the ${}^3{F}_{2,3,4}$, ${}^3{P}_{1,2}$, and ${}^1{G}_4$ states within the $3d^2$ configuration, we derive a nuclear quadrupole moment $Q=-0.222(5)$ b, which is fully consistent with the value recently obtained from molecular data ( J. P. Dognon and P. Pyykkö, Phys. Chem. Chem. Phys. 27, 20453 (2025).).

9 pages