  If neutrons are progressively added to a normal nucleus, the Pauli principle
forces them into states of higher momentum. When the core becomes
neutron-saturated, the nucleus expels most of the wavefunction of the last
neutrons outside to form a halo, which because of its large size can have lower
momentum. It is an open question how nature stabilizes such a fragile system
and provides the glue needed to bind the halo neutrons to the core. Here we
show that this problem is similar to that of the instability of the normal
state of an electron system at zero temperature solved by Cooper, solution
which is at the basis of BCS theory of superconductivity. By mimicking this
approach using, aside from the bare nucleon-nucleon interaction, the long
wavelength vibrations of the nucleus $^{11}$Li, the paradigm of halo nuclei, as
tailored glues of the least bound neutrons, we are able to obtain a unified and
quantitative picture of the observed properties of $^{11}$Li.
