Spectroscopy of $^{50}$Sc and ab initio calculations of $B(M3)$ strengths

TL;DR

This study combines experimental spectroscopy of $^{50}$Sc with ab initio theoretical calculations of $B(M3)$ transition strengths, revealing good agreement for isoscalar transitions but underestimation for isovector ones.

Contribution

It provides the first ab initio calculations of $B(M3)$ strengths in medium-mass nuclei using the in-medium similarity renormalization group approach, compared with detailed experimental data.

Findings

Experimental confirmation of an isomeric $M3$ transition with a $B(M3)$ of 13.6(7) W.u.

Good reproduction of isoscalar $M3$ strengths with bare $g$-factors.

Underestimation of isovector $M3$ strengths by an order of magnitude.

Abstract

The GRIFFIN spectrometer at TRIUMF-ISAC has been used to study excited states and transitions in $^{50}$Sc following the $\beta$-decay of $^{50}$Ca. Branching ratios were determined from the measured $\gamma$-ray intensities, and angular correlations of $\gamma$ rays have been used to firmly assign the spins of excited states. The presence of an isomeric state that decays by an $M3$ transition with a $B(M3)$ strength of 13.6(7)\,W.u. has been confirmed. We compare with the first {\it ab initio} calculations of $B(M3$) strengths in light and medium-mass nuclei from the valence-space in-medium similarity renormalization group approach, using consistently derived effective Hamiltonians and $M3$ operator. The experimental data are well reproduced for isoscalar $M3$ transitions when using bare $g$-factors, but the strength of isovector $M3$ transitions are found to be underestimated by an order of magnitude.