The abnormally large collectivity of neutron-rich magnesium isotopes in the “island of inversion” has not beenwell understood. It has been commented that the unexpectedly large deformations observed in the magnesiumisotopes are attributed to the neutron f7/2 intruder orbits involved remarkably even in the ground states, whichpoints to nuclear force directly. Recently, a new isospin-dependent Nilsson potential was suggested to improvethe calculations of the ground states of magnesium isotopes. With the improved Nilsson potential, in the presentwork we investigate the collectivity of excited states by using the projected shell model. To avoid the collapse ofthe BCS pairing, which occurs in weak pairing, we improved pairing calculations by using the Lipkin-Nogamiapproach. The collectivity and the erosion of the N = 20 shell in neutron-rich magnesium isotopes are discussedby calculating spectra and electric quadrupole transitions. The gyromagnetic factors are calculated and comparedwith existing data to get insight into the configurations of collective states at different spins. A two-quasineutronKπ = 6+ state in 38Mg is predicted to be a possible isomer with an excitation energy lower than the I π = 6+member of the ground-state band.
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