Is the Structure of Si 42 Understood

A more detailed test of the implementation of nuclear forces that drive shell evolution in the pivotal nucleus $^{42}\mathrm{Si}$---going beyond earlier comparisons of excited-state energies---is important. The two leading shell-model effective interactions, SDPF-MU and SDPF-U-Si, both of which reproduce the low-lying $^{42}\mathrm{Si}({2}_{1}^{+})$ energy, but whose predictions for other observables differ significantly, are interrogated by the population of states in neutron-rich $^{42}\mathrm{Si}$ with a one-proton removal reaction from $^{43}\mathrm{P}$ projectiles at $81\text{ }\text{ }\mathrm{MeV}/\mathrm{nucleon}$. The measured cross sections to the individual $^{42}\mathrm{Si}$ final states are compared to calculations that combine eikonal reaction dynamics with these shell-model nuclear structure overlaps. The differences in the two shell-model descriptions are examined and linked to predicted low-lying excited ${0}^{+}$ states and shape coexistence. Based on the present data, which are in better agreement with the SDPF-MU calculations, the state observed at 2150(13) keV in $^{42}\mathrm{Si}$ is proposed to be the (${0}_{2}^{+}$) level.