With the help of a unified nuclear-structure–direct-reaction theory we analyze the reaction ${}^1\mathrm{H}({}^{11}\mathrm{Li},{}^9\mathrm{Li}){}^3\mathrm{H}$. The two halo neutrons are correlated through the bare and the induced (medium polarization) pairing interaction. By considering all dominant reaction channels leading to the population of the $1/2^{-}$ (2.69 MeV) first excited state of ${}^9\mathrm{Li}$, namely, multistep transfer (successive, simultaneous, and nonorthogonality), breakup, and inelastic channels, it is possible to show that the experiment provides direct evidence of phonon mediated pairing.

Absolute values of two-particle transfer cross sections along the Sn-isotopic chain are calculated. They agree with measurements within errors and without free parameters. Within this scenario, the predictions concerning the absolute value of the two-particle transfer cross sections associated with the excitation of the pairing vibrational spectrum expected around the recently discovered closed shell nucleus ${}_{50}{}^{132}\mathrm{Sn}_{82}$ and the very exotic nucleus ${}_{50}{}^{100}\mathrm{Sn}_{50}$ can be considered quantitative, opening new perspectives in the study of pairing in nuclei.

The observed pattern of the population and decay of the superdeformed band of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Dy}$ is related to the large splitting of the giant dipole resonance based on the superdeformed minimum as well as to the low level density associated with it, and to the sudden onset of static pairing correlations taking place at the rotational frequency $\hslash \omega \approx 0.3$ MeV. A new method for spectroscopic studies of superdeformed nuclei is suggested.

The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field by using either a local approximation, which fully takes into account finite size effects, or a contact interaction, with parameters that are quite different from those commonly used in more phenomenological approaches.

We study, within a quantum mechanical framework based on self-consistent mean field theory, the interaction between a vortex and a nucleus immersed in a sea of free neutrons, a scenario representative of the inner crust of neutron stars. Quantal finite size effects force the vortex core outside the nucleus, influencing vortex pinning in an important way