Direct transfer to ${}^{46,48}$K as a survey of the $\ddot{I}€(s_{1/2})$$-\hat{I}½(sdpf)$ interaction

Abstract

The collapse of the canonical $N=28$ magic number in nuclei with $Z<20$ has drawn significant interest as it relates to the emergence of an island of inversion centered on ${}^{42}$Si and ${}^{44}$S. In particular, interactions between the $\ddot{I}€s_{1/2}$ orbital -- empty in ${}^{42}$Si and full in ${}^{44}$S -- and the neutron orbitals just above and below the $N=28$ gap are expected to be critical in this region, but remain relatively unexplored. In this paper, we expand upon the results of our previous study of the direct transfer reaction ${}^{47}$K(d,p${\hat{I}}^3$)${}^{48}$K [C.\,J.~Paxman \textit{et al.}, Phys. Rev. Lett. 134, 162504 (2025)] with the results of the complementary ${}^{47}$K(d,t${\hat{I}}^3$)${}^{46}$K reaction. Through this study, we present a comprehensive scan of the interaction between the critical $\ddot{I}€s_{1/2}$ orbital and a broad range of neutron orbitals spanning nearly two full shells. We identify several discrepancies between the experimental results and state-of-the-art shell model calculations, which suggest a deficiency of the shell model to fully capture the complex proton configuration mixing in this region, highlighting a significant challenge for single-particle descriptions of the island of inversion.

15 pages, 18 figures. To be submitted to Phys. Rev. C