Direct transfer to $^{46,48}$K as a survey of the $\pi(s_{1/2})$$-\nu(sdpf)$ interaction

TL;DR

This study investigates the proton-neutron interactions near the $N=28$ shell closure in potassium isotopes, revealing discrepancies with shell model predictions and highlighting challenges in modeling the island of inversion.

Contribution

It provides a comprehensive experimental survey of the $ ext{π}(s_{1/2})$–$ u(sdpf)$ interaction in $^{46,48}$K, expanding previous transfer reaction studies and identifying limitations of current shell model calculations.

Findings

Discrepancies between experimental data and shell model predictions.

Evidence of complex proton configuration mixing.

Challenges in accurately modeling the island of inversion.

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 $\pi s_{1/2}$ 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$\gamma$)$^{48}$K [C.\,J.~Paxman \textit{et al.}, Phys. Rev. Lett. 134, 162504 (2025)] with the results of the complementary $^{47}$K(d,t$\gamma$)$^{46}$K reaction. Through this study, we present a comprehensive scan of the interaction between the critical $\pi s_{1/2}$ 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.