Models for Pairing Phenomena

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.

arXiv commentContribution to the "Handbook of Nuclear Physics", Springer, 2022, edited by I. Tanihata, H. Toki, and T. Kajino. 32 pages, 5 figures, and 1 table

References in corpus (71)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
• Skyrme-Hartree-Fock-Bogoliubov nuclear mass formulas: Crossing the 0.6 MeV threshold with microscopically deduced pairing
• Pairing in nuclear systems: from neutron stars to finite nuclei
• Radioactive decays at limits of nuclear stability
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Pairing gaps from nuclear mean-field models
• A finite range pairing force for density functional theory in superfluid nuclei
• Microscopic Theory of Nuclear Fission: A Review
• Neutron halo in deformed nuclei
• Odd-Even Staggering of Nuclear Masses: Pairing or Shape Effect?
• The limits of the nuclear landscape explored by the relativistic continuum Hatree-Bogoliubov theory
• Spherical Relativistic Hartree theory in a Woods-Saxon basis
• Halos in medium-heavy and heavy nuclei with covariant density functional theory in continuum
• Microscopic justification of the Equal Filling approximation
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Particle number projection with effective forces
• Overview of Neutron-Proton Pairing
• Odd-even mass differences from self-consistent mean-field theory
• Shell Structure of Exotic Nuclei
• One-quasiparticle States in the Nuclear Energy Density Functional Theory
• Pairing and continuum effects in nuclei close to the drip line
• Particle-Number Restoration within the Energy Density Functional Formalism
• Coexistence of BCS and BEC-like pair structures in halo nuclei
• Two-proton radioactivity
• Symmetry restoration in mean-field approaches
• Evidence for the ground-state resonance of 26O
• Odd-even staggering of binding energies as a consequence of pairing and mean-field effects
• Shrunk halo and quenched shell gap at $N=16$ in ${}^{22}$C: Inversion of $sd$ states and deformation effects
• Symmetry-Projected Hartree-Fock-Bogoliubov Equations
• Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number
• Pairing anti-halo effect
• BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter
• Pairing correlations and resonant states in the relativistic mean field theory
• Effective pairing interactions with isospin density dependence
• Cooper pair transfer in nuclei
• From bound states to the continuum
• Resonant continuum in the Hartree-Fock+BCS approximation
• Many-body effects in nuclear structure
• Study of ground state properties of carbon isotopes with deformed relativistic Hartree-Bogoliubov theory in continuum
• Study of the transition from pairing vibrational to pairing rotational regimes between magic numbers N=50 and N=82, with two-nucleon transfer
• Odd systems in deformed relativistic Hartree Bogoliubov theory in continuum
• Mean-field Based Approaches to Pairing Correlations in Atomic Nuclei
• Rotating deformed halo nuclei and shape decoupling effects
• Empirical pairing gaps, shell effects, and di-neutron spatial correlation in neutron-rich nuclei
• Non-empirical pairing energy functional in nuclear matter and finite nuclei
• Solution of relativistic Hartree-Bogoliubov equations in configurational representation: spherical neutron halo nuclei
• Optimal pair density functional for description of nuclei with large neutron excess
• Quasi-particle continuum and resonances in the Hartree-Fock-Bogoliubov theory
• Non-empirical pairing functional
• Persistent contribution of unbound quasiparticles to the pair correlation in continuum Skyrme-Hartree-Fock-Bogoliubov approach
• Pairing-correlations and particle-number projection methods
• Open problems in theory of nuclear open quantum systems
• Nuclear Halos and Drip Lines in Symmetry-Conserving Continuum HFB Theory
• Gamow-Hartree-Fock-Bogoliubov Method: Representation of quasiparticles with Berggren sets of wave functions
• Adaptive Multi-resolution 3D Hartree-Fock-Bogoliubov Solver for Nuclear Structure
• Intertwined effects of pairing and deformation on neutron halos in magnesium isotopes
• Microscopic Calculation of Fission Product Yields with Particle Number Projection
• Unveiling pairing anti-halo effect in odd-even staggering in reaction cross sections of weakly bound nuclei
• Exact solution of the pairing problem for spherical and deformed systems
• Shell-model-like approach based on cranking covariant density functional theory: bandcrossing and shape evolution in ${}^{60}$Fe
• Approximate particle number projection for finite range density dependent forces
• Evolution of Surface Deformations of Weakly-Bound Nuclei in the Continuum
• Rotational excitations in rare-earth nuclei: a comparative study within three cranking models with different mean fields and the treatments of pairing correlations
• Odd tensor electric transitions in high-spin Sn-isomers and generalized seniority
• Semi-microscopic model of pairing in nuclei
• Generalized-Seniority Pattern and Thermal Properties in Even Sn Isotopes
• Continuum Skyrme-Hartree-Fock-Bogoliubov theory with Green's function method for odd-$A$ nuclei
• Odd-even mass staggering with Skyrme-Hartree-Fock-Bogoliubov theory
• Neutron drip line of $Z=9-11$ isotopic chains
• Shell-model-like approach based on cranking covariant density functional theory with a separable pairing force