  We compute the proton-neutron entanglement entropy in the interacting nuclear
shell model for a variety of nuclides and interactions. Some results make
intuitive sense, for example that the shell structure, as governed by
single-particle and monopole energies, strongly affects the energetically
available space and thus the entanglement entropy. We also find a surprising
result: that the entanglement entropy at low excitation energy tends to
decrease for nuclides when $N \neq Z$. While we provide evidence this arises
from the physical nuclear force by contrasting with random two-body
interactions which shows no such decrease, the exact mechanism is unclear.
Nonetheless, the low entanglement suggests that in models of neutron-rich
nuclides, the coupling between protons and neutrons may be less computationally
demanding than one might otherwise expect.
