  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.
