Probing exotic cross-shell interactions at N=28 with single-neutron transfer on 47K

We present the first measurement of the ${}^{47}$K($d,p\gamma$)${}^{48}$K transfer reaction, performed in inverse kinematics using a reaccelerated beam of ${}^{47}$K. The level scheme of ${}^{48}$K has been greatly extended with nine new bound excited states identified and spectroscopic factors deduced. Detailed comparisons with SDPF-U and SDPF-MU shell-model calculations reveal a number of discrepancies with these results, and a preference for SDPF-MU is found. Intriguingly, an apparent systematic overestimation of spectroscopic factors and a poor reproduction of the energies for 1${}^{-}$ states suggests that the mixing between the $\pi s_{1\mathrm{/}2}^1{d}_{3\mathrm{/}2}^4$ and $\pi s_{1\mathrm{/}2}^2{d}_{3\mathrm{/}2}^3$ proton configurations in ${}^{48}$K is not correctly described using current interactions, challenging our descriptions of light $N=28$ nuclei.