Pairing strength on the nuclear size in relativistic continuum Hartree-Bogoliubov theory

TL;DR

This paper investigates how pairing correlations influence nuclear size and halo formation in neutron-rich nuclei using relativistic continuum Hartree-Bogoliubov theory, highlighting the dual role of pairing in modifying orbit radii and occupation probabilities.

Contribution

It demonstrates the complex impact of pairing strength on nuclear size and halo formation, emphasizing the role of weakly-bound low-l orbits in these phenomena.

Findings

Pairing correlations can both reduce and increase nuclear radii.

Enhanced pairing can lead to nuclear halo formation even without individual orbit proximity to the continuum.

The effect of pairing on nuclear size is more significant in weakly-bound nuclei.

Abstract

The influence of pairing correlations on the nuclear size and in particular on the formation of nuclear halos is studied in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. It turns out that the contributions from the weakly-bound orbits with low orbital angular momenta $l$ play an important role. As an example, we investigate the neutron-rich Mg isotopes as a function of the pairing strength in situations, where the neuron Fermi surface are below, between and above two weakly-bound $2p$ levels. We find that the size of the pairing correlations has a two-fold influence on the density distribution of the neutrons and therefore on the total nuclear size. First it can change the root mean square (rms) radius of the individual weakly-bound orbits and second it can enhance the occupation probabilities of these orbits in the nuclear system. On one side increasing pairing correlations reduce the rms radii of the orbits with small orbital angular momenta close to the continuum limit (pairing anti-halo effect), on the other side they also can lead to an enhanced occupation of low-$l$ orbits above the Fermi surface producing in this way a strong increase of the total radius of the nuclear system. As a consequence, a nuclear halo can form even in cases, where non of the individual low-$l$ orbits is very close to the continuum. This leads to the fact that compared with well-bound nuclei, the impact of the pairing strength on the nuclear size is more pronounced in weakly-bound nuclei than in well-bound systems.