Measurement of an unusually large magnetic octupole moment in $^{45}$Sc challenges state-of-the-art nuclear-structure theory

We measure the hyperfine $C$-constant of the $3d4s^2 ~^2D_{5/2}$ atomic state in $^{45}$Sc: $C=-0.25(12)$,kHz. High-precision atomic calculations of the hyperfine structure of the $3d4s^2 ~^2D_{5/2}$ state and second-order corrections are performed to infer the nuclear magnetic octupole moment $Omega = 1.6(8) mu_N b$. With a single valence proton outside of the doubly-magic calcium core, this element is ideally suited for an in-depth study of the many intriguing nuclear structure phenomena observed within the neighboring isotopes of calcium. We compare $Omega$ to shell-model calculations, and find that they cannot reproduce the experimental value of $Omega$ for $^{45}$Sc. We furthermore explore the use of Density Functional Theory for evaluating $Omega$, and obtain values in line with the shell-model calculations. This work provides a crucial step in guiding future measurements of this fundamental quantity on radioactive scandium isotopes and will hopefully motivate a renewed experimental and theoretical interest.