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 $Q = 0.222(2)$ b, which is fully consistent with the value recently obtained from molecular data ( J. P. Dognon and P. Pyykk\"{o}, Phys. Chem. Chem. Phys. 27, 20453 (2025).).