Pairing in nuclear systems: from neutron stars to finite nuclei

This review treats several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. It focuses on the links between many-body pairing, as it evolves from the underlying nucleon-nucleon interaction into experimental and theoretical manifestations of superfluidity in infinite nuclear matter, and pairing in finite nuclei. The nature of pair correlations in nuclei and their potential impact on nuclear structure experiments is discussed, as is recent experimental evidence that suggests a connection between pairing and phase transitions (or transformations) in finite nuclear systems. Finally, the article considers recent investigations of ground-state properties of random two-body interactions in which pairing plays a minor role, although the interactions yield interesting nuclear properties such as $0^{+}$ ground states in even-even nuclei.