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

The GRIFFIN spectrometer at TRIUMF-ISAC has been used to study excited states and transitions in ${}^{50}\mathrm{Sc}$ following the $\beta$ decay of ${}^{50}\mathrm{Ca}$. 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 $B\left(M3\right)$ strength of 13.6(7) W.u. has been confirmed. We compare the first 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 effective $M3$ 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.

Figure 1

Level scheme of the levels observed in ${}^{50}\mathrm{Sc}$ following the $\beta$ decay of ${}^{50}\mathrm{Ca}$. The width of the arrows represent the relative total intensity of the transition measured in this work. The positioning of the levels have been modified for easier visualization.

Figure 2

$\gamma$-ray energy spectrum in coincidence with the 1519-keV transition. The 328-keV branch is observed for the first time with a $\gamma$-ray branching ratio of 0.78(8)%.

Figure 3

The $\gamma \text{−}\gamma$ angular correlation of the $1519\to 71$-keV cascade indicating an ($E2/M1$) mixing ratio of +0.015(25) for the 71-keV transition, and firmly assigning the spins of the 257- and 328-keV states as $2^{+}$ and $3^{+}$ respectively.