$\beta$ Decay and Isomeric Properties of Neutron-Rich Ca and Sc Isotopes

The isomeric and $\beta$-decay properties of neutron-rich ${}^{53-57}$Sc and ${}^{53,54}$Ca nuclei near neutron number $N$=32 are reported, and the low-energy level schemes of ${}^{53,54,56}$Sc and ${}^{53-57}$Ti are presented. The low-energy level structures of the ${}_{21}$Sc isotopes are discussed in terms of the coupling of the valence $1f_{7\mathrm{/}2}$ proton to states in the corresponding ${}_{20}$Ca cores. Implications with respect to the robustness of the $N$=32 subshell closure are discussed, as well as the repercussions for a possible $N$=34 subshell closure.