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

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.

19 pages, 5 tables, 4 figures, 1 appendix with 3 pages, 47 references

References in corpus (6)

• Recent development of complex scaling method for many-body resonances and continua in light nuclei
• Measurement of two-halo neutron transfer reaction p(${}^{11}$Li,${}^9$Li)t at 3$A$ MeV
• Roles of the tensor and pairing correlations on the halo formation in 11Li
• Charge radii and electromagnetic moments of Li and Be isotopes from the ab initio no-core shell model
• ${}^4\mathrm{He}$+$n$+$n$ continuum within an ab initio framework
• Pairing in the continuum: the quadrupole response of the Borromean nucleus 6He

Cited by in corpus (1)

• Pairing enhancement in a two-neutron transfer process through the continuum