Precision measurement of the magnetic octupole moment in 45Sc as a test for state-of-the-art atomic- and nuclear-structure theory

We report on measurements of the hyperfine $A, B$ and $C$-constants of the $3d4s^2 ~^2D_{5/2}$ and $3d4s^2 ~^2D_{3/2}$ atomic states in $^{45}$Sc. High-precision atomic calculations of the hyperfine fields of these states and second-order corrections are performed, and are used to extract $C_{5/2}=-0.06(6)$ kHz and $C_{3/2}=+0.04(3)$ kHz from the data. These results are one order of magnitude more precise than the available literature. From the combined analysis of both atomic states, we infer the nuclear magnetic octupole moment $\Omega = -0.07(53) \mu_N b$, including experimental and atomic structure-related uncertainties. With a single valence proton outside of a magic calcium core, scan…