One-particle properties of deformed N $\approx$ 28 odd-N nuclei with weakly-bound or resonant neutrons

TL;DR

This paper investigates the deformation and single-particle properties of neutron-rich odd-N nuclei near N=28 using deformed Woods-Saxon potentials and solving the Schrödinger equation, revealing potential deformation and specific ground state characteristics.

Contribution

It introduces a method to accurately calculate weakly-bound and resonant states in deformed nuclei near the neutron drip line, highlighting the impact of potential diffuseness on energy levels.

Findings

N=28 energy gap diminishes near the drip line

Ground states of certain nuclei are likely deformed

Resonant states in Mg-39 may have 5/2− spin-parity

Abstract

Possible deformation of odd-N nuclei with N $\approx$ 28 towards the neutron drip line is investigated using the Nilsson diagram based on deformed Woods-Saxon potentials. Both weakly-bound and resonant one-particle levels are properly obtained by directly solving the Schr\"{o}dinger equation in mesh of space coordinate with the correct boundary condition. If we use the same diffuseness of the potential as that of $\beta$-stable nuclei, the energy difference between the neutron 2p$_{3/2}$ and 1f$_{7/2}$ levels becomes very small or the N=28 energy gap almost disappears, as the binding energies of those levels approach zero. This suggests that the ground states of those neutron drip line nuclei are likely to be deformed. In particular, the spin-parity and the magnetic moment of the ground state of odd-N nuclei, $^{43}_{16}$S$_{27}$ and $^{45}_{16}$S$_{29}$, are examined. Moreover, it is suggested that in $^{39}_{12}$Mg$_{27}$ lying outside the drip line the lowest resonant state may have 5/2$^{-}$, if the N=28 energy gap almost vanishes.