Enormous nuclear surface diffuseness of Ne and Mg isotopes in the island of inversion

Background: The density profile of exotic nuclei can be a rich source of information on the nuclear surface. In particular, the nuclear surface diffuseness is correlated with the occupation probability of nucleons in distinct nuclear orbits, especially those with low angular momenta.

Purpose: 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.

Method: We use the microscopic antisymmetrized molecular dynamics model to calculate the densities and other spectroscopic information related to Ne and Mg isotopes. A two-parameter Fermi density distribution is then used to define the diffuseness parameter and the matter radius. These quantities are extracted by minimizing the difference between these two densities. To relate them with observables, the two densities are given as inputs to a Glauber model calculation of nucleon-nucleus elastic scattering differential cross section, with the demand that they reproduce the first peak position and its magnitude.

Results: 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 surface diffuseness is strongly correlated with the nuclear deformation, in the island of inversion, and gradually increases with the occupation of neutrons in the $1p_{3/2}$ orbit. This result is also confirmed by a single-particle estimate of the valence neutron density distribution, with ${}^{29}\mathrm{Ne}$ as a test case. An exception is noted for ${}^{35–37}\mathrm{Mg}$, where the filling up of the holes in the $sd$ shell partially compensates the increase in diffuseness due to filling up of the $1p_{3/2}$ orbit.

Conclusion: 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 $1p_{3/2}$ orbit.

Figure 1

Nuclear matter density distributions of ${}^{29}\mathrm{Ne}$ by AMD and the one approximated by the 2pF function.

Figure 2

Nuclear surface diffuseness of Ne and Mg isotopes as a function of neutron number.

Figure 3

Schematic illustrations of the $m\mathrm{p}n$h configurations relative to the $N=20$ shell closure. The circles indicate the particles in $pf$ shell while the crosses indicate the holes in $sd$ shell.

Figure 4

A schematic Nilsson diagram for prolate deformation.

Figure 5

Nuclear diffuseness parameters extracted from density distributions obtained by the single-particle model for $N>18$. The AMD results (Fig. 2) are also plotted for comparison.

Figure 6

Valence neutron density distribution and its decomposition into particle $1p_{3/2}$ and $0f_{7/2}$ states and $0d_{3/2}$ hole state. See text for details. A vertical thin dotted line denotes the radius parameter value 3.13, extracted from the density distribution obtained by the single-particle model.