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 $3d4s\,^3\text{D}_2$\,$\leftrightarrow$\,$3d4p\,^3\text{F}^\circ_3$ 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 $μ$\,=\,$+5.57(4)(2)\,μ_N$ and $Q$\,=\,$+42(38)(28)\,e^2\;{\rm fm^2}$, 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.