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Weak binding effects on the structure of $^{40}$Mg

While the phenomenon of one- and two-neutron ground-state halo nuclei is well established, the effects of weak binding on nuclear excitation properties remain largely unexplored. Motivated by this question and by recent data in $^{40}$Mg we investigate the coupling of weakly bound (halo) valence neutrons to a core using the known properties of $^{40}$Mg to explore and illustrate possible particle-core coupling schemes and their impact on the low-lying excitation spectrum.