Spatial structure of Cooper pairs in nuclei

TL;DR

This paper investigates the spatial structure of neutron Cooper pairs in dilute neutron matter and neutron-rich nuclei, revealing their compactness and strong spatial correlations, especially near the BCS-BEC crossover and in low-density regions.

Contribution

It provides a detailed analysis of the spatial characteristics of neutron Cooper pairs using BCS and HFB models, highlighting their compactness and correlation properties in various density regimes.

Findings

Neutron Cooper pairs are spatially compact, smaller than interparticle distance.

Pair size reaches minimum (~5 fm) at low densities (~10^{-1} of saturation density).

Strong spatial correlations favoring small relative distances are observed in finite neutron-rich nuclei.

Abstract

We discuss the spatial structure of the Cooper pair in dilute neutron matter and neutron-rich nuclei by means of the BCS theory and the Skyrme-Hartree-Fock-Bogioliubov model, respectively. The neutron pairing in dilute neutron matter is close to the region of the BCS-BEC crossover in a wide density range, giving rise to spatially compact Cooper pair whose size is smaller than the average interaparticle distance. This behavior extends to moderate low density ($\sim 10^{-1}$ of the saturation density) where the Cooper pair size becomes smallerst ($\sim 5$ fm). The Cooper pair in finite nuclei also exhibits the spatial correlation favoring the coupling of neutrons at small relative distances $r \lesim 3$ fm with large probability. Neutron-rich nuclei having small neutron separation energy may provide us opportunity to probe the spatial correlation since the neutron pairing and the spatial correlation persists also in an area of low-density neutron distribution extending from the surface to far outside the nucleus.