Models for Pairing Phenomena

TL;DR

This paper reviews pairing phenomena in nuclear systems, discussing theoretical models like BCS and Bogoliubov transformations, and addressing particle number conservation and continuum effects in exotic nuclei.

Contribution

It provides a comprehensive overview of nuclear pairing models, emphasizing basic ideas and recent approaches for particle number conservation and continuum contributions.

Findings

Comparison of pairing models in nuclear physics

Discussion of particle number projection techniques

Analysis of continuum effects in exotic nuclei

Abstract

Pairing effects manifests themselves in many aspects in nuclear systems ranging from finite nuclei to nuclear matter and compact stars. Although with some specific features for nuclear systems, the mechanism of pairing between nucleons in these systems resembles that of electrons in superconductors. The Bardeen-Cooper-Schrieffer (BCS) theory, the first successful and microscopic theory for superconductivity, and the Bogoliubov transformation, the generalization of the BCS theory, have been widely used to describe pairing correlations in nuclear systems. To deal with the problem of particle number non-conservation in the BCS method and generalized Bogoliubov transformation, particle number projection techniques as well as several approaches which keep the particle number conserved, have been proposed. In the study of exotic nuclei, which are quantum open systems, the continuum contributions have to be taken into account. In this chapter, a thorough but brief discussion of pairing effects in nuclear systems will be introduced. Then nuclear models dealing with pairing correlations in nuclear structure properties will be presented to different extent of details. Although formulas are given, the emphasis is mainly put on the basic ideas concerning these models.