The density profile of exotic nuclei can be a rich source of information on the nuclear surface. In particular, the nuclear surface diffuseness parameter is correlated with the occupation probability of nucleons indistinct nuclear orbits, especially those with low angular momenta. The aim of this paper is to investigate the relationship between the nuclear surface diffuseness and spectroscopic information of neutron rich Ne and Mg isotopes both at the cusp and inside the island of inversion. We use the microscopic antisymmetrized molecular dynamics model to calculate these densities and other spectroscopic information. A two-parameter Fermi density distribution is then used to define the diffuseness parameter. To relate them with observables, the nucleon-nucleus elastic scattering differential cross section is calculated with the demand that they reproduce the first peak position and its magnitude. A marked increase in the occupation of neutrons in the pf-orbit is noted in Ne and Mg isotopes from N=19 onwards. We observed that the nuclear diffuseness is strongly correlated with the nuclear deformation, in the island of inversion, and gradually increases with the occupation of neutrons in the 1p3/2 orbit. This result is also confirmed by a single-particle estimate of the valence neutron density distribution. An exception is noted for 35-37Mg, where the filling up of the holes in the sd-shell partially compensates the increase in diffuseness due to filling up of the 1p3/2 orbit. Information on nuclear density profile of neutron rich medium mass nuclei can be reliably extracted by studying the first diffraction peak of the nucleon-nucleus elastic scattering differential cross section. The enormous surface diffuseness of Ne and Mg isotopes, in the island of inversion, could be attributed to the increasing neutron occupation of the 1p3/2 orbit.
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