Bound states of the neutron-deficient, near-dripline nucleus ${}^{36}\mathrm{Ca}$ were populated in two-neutron removal from the ground state of ${}^{38}\mathrm{Ca}$, a direct reaction sensitive to the single-particle configurations and couplings of the removed neutrons in the projectile wave function. Final-state exclusive cross sections for the formation of ${}^{36}\mathrm{Ca}$ and the corresponding longitudinal momentum distributions, both determined through the combination of particle and $\gamma$-ray spectroscopy, are compared to predictions combining eikonal reaction theory and shell-model two-nucleon amplitudes from the USDB, USDC, and ZBM2 effective interactions. The final-state cross-section ratio $\sigma \left(2_1^{+}\right)/\sigma \left(0^{+}\right)$ shows particular sensitivity and is approximately reproduced only with the two-nucleon amplitudes from the ZBM2 effective interaction that includes proton cross-shell excitations into the $pf$ shell. Characterizing the proton $pf$-shell occupancy locally and schematically, an increase of the $sd-pf$ shell gap by 250 keV yields an improved description of this cross-section ratio and simultaneously enables a reproduction of the $B(E2;0_1^{+}\to 2_1^{+})$ excitation strength of ${}^{36}\mathrm{Ca}$. This highlights an important aspect if a new shell-model effective interaction for the region was to be developed on the quest to model the neutron-deficient Ca isotopes and surrounding nuclei whose structure is impacted by proton cross-shell excitations.

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• Direct reactions
• Nuclear reactions
• Nuclear structure & decays
• Shell model
• 20 ≤ A ≤ 38
• Radioactive beams
• Spectrometers & spectroscopic techniques