Ground State Magnetic Dipole Moment of ${}^{40}$Sc

Abstract

The hyperfine coupling constants of the proton dripline odd-odd ${}^{40}$Sc nucleus were deduced from the hyperfine spectrum of the $3d4s{}^3{\text{D}}_2$\,$\leftrightarrow$\,$3d4p{}^3{\text{F}}_3^{\circ }$ transition in Sc II, measured by the bunched beam collinear laser spectroscopy technique. The ground state magnetic dipole and electric quadrupole moments were determined for the first time as $\mu$\,=\,$+5.57(4)(2){\mu }_N$ and $Q$\,=\,$+42(38)(28)e^2\mathrm{f}{\mathrm{m}}^2$, respectively. The magnetic moment is well reproduced by the additivity rule with magnetic moments of neighboring odd-even nuclei in the vicinity of the doubly-magic ${}^{40}$Ca nucleus. An ab-initio multishell valence-space Hamiltonian was also employed to calculate the magnetic moment of ${}^{40}$Sc, which spans across the $sd$ and $fp$ nuclear shells, where we obtained good agreements.