A Borromean nucleus is a bound three-body system which is pairwise unboundbecause none of the two-body subsystem interactions are strong enough to bindthem in pairs. As a consequence, the single-particle spectrum of a neutron inthe core of a Borromean nucleus is purely continuum, similarly to the spectrumof a free neutron, but two valence neutrons are bound up in such a core. Mostof the usual approaches do not use the true continuum to solve the three-bodyproblem but use a discrete basis, like for example, wave functions in a finitebox. In this paper the proper continuum is used to solve the pairingHamiltonian in the continuum spectrum of energy by using the single particlelevel density devoid of the free gas. It is shown that the density defined inthis way modulates the pairing in the continuum. The partial-wave occupationprobabilities for the Borromean nuclei $^6$He and $^{11}$Li are calculated as afunction 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 smallstrength the $(s_{1/2})^2$ configuration becomes the dominant in both Borromeannuclei. At the physical strength, the calculated wave function amplitudes showa good agreement with other methods and experimental data which indicates thatthis simple model grasps the essence of the pairing in the continuum.
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