Pairing correlations in exotic nuclei

TL;DR

This paper explores pairing correlations in exotic nuclei using BCS and HFB theories, demonstrating their effects on nuclear properties and reaction cross sections, and proposing effective interactions for better modeling.

Contribution

It introduces a comprehensive application of pairing theories to exotic nuclei, including novel effective density-dependent interactions that improve modeling accuracy.

Findings

Reproduced odd-even staggering in reaction cross sections.

Demonstrated correlation between separation energy and anti-halo effect.

Proposed effective pairing interactions matching scattering length and pairing gaps.

Abstract

The BCS and HFB theories which can accommodate the pairing correlations in the ground states of atomic nuclei are presented. As an application of the pairing theories, we investigate the spatial extension of weakly bound Ne and C isotopes by taking into account the pairing correlation with the Hartree-Fock-Bogoliubov (HFB) method and a 3-body model, respectively. We show that the odd-even staggering in the reaction cross sections of $^{30,31,32}$Ne and $^{14,15,16}$C are successfully reproduced, and thus the staggering can be attributed to the unique role of pairing correlations in nuclei far from the stability line. A correlation between a one-neutron separation energy and the anti-halo effect is demonstrated for $s$- and p-waves using the HFB wave functions. We also propose effective density-dependent pairing interactions which reproduce both the neutron-neutron ($nn$) scattering length at zero density and the neutron pairing gap in uniform matter. Then, we apply these interactions to study pairing gaps in semi-magic finite nuclei, such as Ca, Ni, Sn and Pb isotopic chains.