# Cooper pairs in the Borromean nuclei $^6$He and $^{11}$Li using continuum single particle level density

## TL;DR

This paper investigates pairing correlations in Borromean nuclei $^6$He and $^{11}$Li using a continuum single particle level density approach, revealing how pairing influences their structure and configurations.

## Contribution

It introduces a method to incorporate the true continuum spectrum in pairing calculations using a single particle level density, improving understanding of Borromean nuclei.

## Key findings

- The continuum density modulates pairing in Borromean nuclei.
- Configuration dominance varies with pairing strength.
- Results agree with experimental data and other models.

## Abstract

A Borromean nucleus is a bound three-body system which is pairwise unbound because none of the two-body subsystem interactions are strong enough to bind them in pairs. As a consequence, the single-particle spectrum of a neutron in the core of a Borromean nucleus is purely continuum, similarly to the spectrum of a free neutron, but two valence neutrons are bound up in such a core. Most of the usual approaches do not use the true continuum to solve the three-body problem but use a discrete basis, like for example, wave functions in a finite box. In this paper the proper continuum is used to solve the pairing Hamiltonian in the continuum spectrum of energy by using the single particle level density devoid of the free gas. It is shown that the density defined in this way modulates the pairing in the continuum. The partial-wave occupation probabilities for the Borromean nuclei $^6$He and $^{11}$Li are calculated as a function of the pairing strength. While at the threshold strength the $(s_{1/2})^2$ and $(p_{3/2})^2$ configurations are equally important in $^6$He, the $(s_{1/2})^2$ configuration is the main one in $^{11}$Li. For very small strength the $(s_{1/2})^2$ configuration becomes the dominant in both Borromean nuclei. At the physical strength, the calculated wave function amplitudes show a good agreement with other methods and experimental data which indicates that this simple model grasps the essence of the pairing in the continuum.