  Finite nuclei such as those found in the chain of even tin isotopes from
^{102}Sn to ^{130}Sn, exhibit a near constancy of the 2^+_1-0^+_1 excitation
energy, a constancy which can be related to strong pairing correlations and the
near degeneracy in energy of the relevant single particle orbits. Large
shell-model calculations for these isotopes reveal that the major contribution
to pairing correlations in the tin isotopes stems from the ^1S_0 partial wave
in the nucleon-nucleon interaction. Omitting this partial wave and the ^3P_2
wave in the construction of an effective interaction, results in a spectrum
which has essentially no correspondence with experiment. These partial wave are
also of importance for infinite neutron matter and nuclear matter and give the
largest contribution to the pairing interaction and energy gap in neutron star
matter.
