  Recent data resulting from studies of two-nucleon transfer reaction on 11Li,
analyzed through a unified nuclear-structure-direct-reaction theory have
provided strong direct as well as indirect confirmation, through the population
of the first excited state of 9Li and of the observation of a strongly quenched
ground state transition, of the prediction that phonon mediated pairing
interaction is the main mechanism binding the neutron halo of the 8.5 ms-lived
11Li nucleus. In other words, the ground state of 11Li can be viewed as a
neutron Cooper pair bound to the 9Li core, mainly through the exchange of
collective vibration of the core and of the pigmy resonance arizing from the
sloshing back and forth of the neutron halo against the protons of the core,
the mean field leading to unbound two particle states, a situation essentially
not altered by the bare nucleon-nucleon interaction acting between the halo
neutrons. Two-neutron pick-up data, together with (t,p) data on 7Li, suggest
the existence of a pairing vibrational band based on 9Li, whose members can be
excited with the help of inverse kinematic experiments as was done in the case
of 11Li(p,t)9Li reaction. The deviation from harmonicity can provide insight
into the workings of medium polarization effects on Cooper pair nuclear
pairing, let alone specific information concering the "rigidity" of the N=6
shell closure. Further information concerning these questions is provided by
the predicted absolute differential cross sections associated with the
reactions 12Be(p,t)10Be(gs) and 12Be(p,t)10Be(pv)(~10Be(p,t)8Be(gs)). In
particular, concerning this last reaction, predictions of \sigma_{abs} can
change by an order of magnitude depending on whether the halo properties
associated with the d_{5/2} orbital are treated selfconsistently in calculating
the ground state correlations of the (pair removal) mode, or not.
