Role of deformation in odd-even staggering in reaction cross sections for $^{30,31,32}$Ne and $^{36,37,38}$Mg isotopes

TL;DR

This paper investigates how ground state deformation and pairing anti-halo effects influence the odd-even staggering observed in reaction cross sections of certain neutron-rich isotopes, highlighting the importance of pairing correlations.

Contribution

It introduces a combined approach using deformed Woods-Saxon potential and Hartree-Fock-Bogoliubov method to analyze deformation and pairing effects on reaction cross sections.

Findings

Odd-even staggering persists with deformation when one-neutron separation energy is small.

Pairing anti-halo effect significantly contributes to the staggering.

Deformation reduces but does not eliminate the staggering.

Abstract

We discuss the role of pairing anti-halo effect in the observed odd-even staggering in reaction cross sections for $^{30,31,32}$Ne and $^{36,37,38}$Mg isotopes by taking into account the ground state deformation of these nuclei. To this end, we construct the ground state density for the $^{30,31}$Ne and $^{36,37}$Mg nuclei based on a deformed Woods-Saxon potential, while for the $^{32}$Ne and $^{38}$Mg nuclei we also take into account the pairing correlation using the Hartree-Fock-Bogoliubov method. We demonstrate that, when the one-neutron separation energy is small for the odd-mass nuclei, a significant odd-even staggering still appears even with finite deformation, although the degree of staggering is somewhat reduced compared to the spherical case. This implies that the pairing anti-halo effect in general plays an important role in generating the odd-even staggering in reaction cross sections for weakly bound nuclei.