Introduction

Nucleonic pairing is a ubiquitous phenomenon underlying many aspects of structure and dynamics of atomic nuclei and extended nuclear matter[1,2]. The crucial role of nucleonic superfluidity lies in its emergent nature. Indeed, while the correlation energy due to pairing is a small correction to the nuclear binding energy, the superfluid wave function represents an entirely different phase described by new quasiparticle degrees of freedom. The road to this new phase is associated with a phase transition connected with a symmetry breaking, and this underpins the nonperturbative nature of pairing.

Many facets of nucleonic superfluidity - including those related to phenomenology and theory of pairing - are discussed in this volume [3]. Here, we outline several aspects of nucleonic superfluidity within the framework of the nuclear density functional theory (DFT). The main building blocks of nuclear DFT are the effective mean fields, often represented by local nucleonic densities and currents. When compared to the electronic DFT for the superconducting state[4,5,6] the unique features of the nuclear variant are (i) the presence of two kinds of fermions, protons and neutrons, (ii) the absence of external potential, and (iii) the need for symmetry restoration in a finite self-bound system. In the context of pairing, nuclear superfluid DFT is a natural extension of the traditional BCS theory for electrons [7] and nucleons[8], and a tool of choice for describing complex, open-shell nuclei.

At the heart of nuclear DFT lies the energy density functional (EDF). The requirement that the total energy be minimal under a variation of the densities leads to the Hartree-Fock-Bogoliubov (HFB; or Bogoliubov-de Gennes) equations. The quasiparticle vacuum associated with the HFB solution is a highly correlated state that allows a simple interpretation of various phenomena it the language of pairing mean fields and associated order parameters.

This paper is organized as follows. Section 2 describes the essentials of the general pair-condensate state. The HFB theory is outlined in Sec. 3. The Bogoliubov sea, related to the quasiparticle-quasihole symmetry of the HFB Hamiltonian is discussed in Sec. 4 and Sec. 5 is devoted to the form of the nuclear pairing EDF. The quasiparticle energy spectrum of HFB contains both discrete bound states and continuum unbound states. The properties of the associated quasiparticle continuum are reviewed in Sec. 7. Section 8 describes the extension of the HFB formalism to odd-particle systems and quasiparticle blocking. Finally, conclusions are contained in Sec. 9.