In this work, we employ quantum entanglement entropy to study the evolution of nuclear shell structures. We focus on using single-orbital entropy and total entanglement entropy to explore the stability and evolution of shell structures in neutron-rich nuclei, particularly along the oxygen and calcium isotopic chains. By performing shell model calculations, we derive occupation numbers and compute entanglement metrics to shed light on the emergence and disappearance of magic numbers. The behavior of the entanglement entropy was investigated in the vicinity of the islands of inversion at neutron numbers $N$ = 40 and $N$ = 50, with particular attention to the Cr, Fe, and Ni isotones. Our findings underscore the critical role of quantum entanglement in understanding shell closures, revealing exotic structural features such as new magic numbers and shell evolution in neutron-rich regions.

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• Entanglement entropy
• Nuclear structure & decays
• Nuclear many-body theory
• Shell model