Is the structure of 42Si understood

A more detailed test of the implementation of nuclear forces that drive shell evolution in the pivotal nucleus \nuc{42}{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 \nuc{42}{Si}($2^+_1$) energy, but whose predictions for other observables differ significantly, are interrogated by the population of states in neutron-rich \nuc{42}{Si} with a one-proton removal reaction from \nuc{43}{P} projectiles at 81~MeV/nucleon. The measured cross sections to the individual \nuc{42}{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 \nuc{42}{Si} is proposed to be the ($0^+_2$) level.